You are an expert Python programmer. Write correct, efficient Python 3 code that solves the problem and passes all tests. Output the code in the following format: ```python
<code>
```

PROBLEM:
Given an array nums of n integers, your task is to find the maximum value of k for which there exist two adjacent subarrays of length k each, such that both subarrays are strictly increasing. Specifically, check if there are two subarrays of length k starting at indices a and b (a < b), where:

Both subarrays nums[a..a + k - 1] and nums[b..b + k - 1] are strictly increasing.
The subarrays must be adjacent, meaning b = a + k.

Return the maximum possible value of k.
A subarray is a contiguous non-empty sequence of elements within an array.

Example 1:

Input: nums = [2,5,7,8,9,2,3,4,3,1]
Output: 3
Explanation:

The subarray starting at index 2 is [7, 8, 9], which is strictly increasing.
The subarray starting at index 5 is [2, 3, 4], which is also strictly increasing.
These two subarrays are adjacent, and 3 is the maximum possible value of k for which two such adjacent strictly increasing subarrays exist.

Example 2:

Input: nums = [1,2,3,4,4,4,4,5,6,7]
Output: 2
Explanation:

The subarray starting at index 0 is [1, 2], which is strictly increasing.
The subarray starting at index 2 is [3, 4], which is also strictly increasing.
These two subarrays are adjacent, and 2 is the maximum possible value of k for which two such adjacent strictly increasing subarrays exist.

Constraints:

2 <= nums.length <= 2 * 105
-109 <= nums[i] <= 109

Your solution to the problem should be a method of the class Solution called maxIncreasingSubarrays and should pass all tests. Use the following starter code:
```python
class Solution:
    def maxIncreasingSubarrays(self, nums: List[int]) -> int:
        # Add your code here
```

SOLUTION:

Question:
PROBLEM:
Given an array nums of n integers, your task is to find the maximum value of k for which there exist two adjacent subarrays of length k each, such that both subarrays are strictly increasing. Specifically, check if there are two subarrays of length k starting at indices a and b (a < b), where:

Both subarrays nums[a..a + k - 1] and nums[b..b + k - 1] are strictly increasing.
The subarrays must be adjacent, meaning b = a + k.

Return the maximum possible value of k.
A subarray is a contiguous non-empty sequence of elements within an array.

Example 1:

Input: nums = [2,5,7,8,9,2,3,4,3,1]
Output: 3
Explanation:

The subarray starting at index 2 is [7, 8, 9], which is strictly increasing.
The subarray starting at index 5 is [2, 3, 4], which is also strictly increasing.
These two subarrays are adjacent, and 3 is the maximum possible value of k for which two such adjacent strictly increasing subarrays exist.

Example 2:

Input: nums = [1,2,3,4,4,4,4,5,6,7]
Output: 2
Explanation:

The subarray starting at index 0 is [1, 2], which is strictly increasing.
The subarray starting at index 2 is [3, 4], which is also strictly increasing.
These two subarrays are adjacent, and 2 is the maximum possible value of k for which two such adjacent strictly increasing subarrays exist.

Constraints:

2 <= nums.length <= 2 * 105
-109 <= nums[i] <= 109

Your solution to the problem should be a method of the class Solution called maxIncreasingSubarrays and should pass all tests. Use the following starter code:
```python
class Solution:
    def maxIncreasingSubarrays(self, nums: List[int]) -> int:
        # Add your code here
```

SOLUTION:

assert Solution().maxIncreasingSubarrays(nums = [1,3,2,4,3,5,4,6,5,7]) == 2

assert Solution().maxIncreasingSubarrays(nums = [1,3,5,7,9,11,13,15]) == 4

assert Solution().maxIncreasingSubarrays(nums = [10,20,30,25,35,45,55,65,75]) == 3

assert Solution().maxIncreasingSubarrays(nums = [1,2,2,3,4,5,6,7,8,9]) == 4

assert Solution().maxIncreasingSubarrays(nums = [2,5,7,8,9,2,3,4,3,1]) == 3

assert Solution().maxIncreasingSubarrays(nums = [10,9,8,7,6,5,4,3,2,1]) == 1

assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10]) == 5

assert Solution().maxIncreasingSubarrays(nums = [1,2,3,1,2,3,1,2,3,1]) == 3

assert Solution().maxIncreasingSubarrays(nums = [1,2,3,2,3,4,5,4,5,6]) == 3

assert Solution().maxIncreasingSubarrays(nums = [5,6,7,8,9,10,11,12,13,14,15]) == 5

assert Solution().maxIncreasingSubarrays(nums = [1,3,5,7,9,11,13,15,17,19]) == 5

assert Solution().maxIncreasingSubarrays(nums = [1,3,5,7,9,2,4,6,8,10]) == 5

assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,3,4,5,6,7]) == 5

assert Solution().maxIncreasingSubarrays(nums = [1,1,1,1,1,1,1,1,1,1]) == 1

assert Solution().maxIncreasingSubarrays(nums = [1,2,1,2,1,2,1,2,1,2]) == 2

assert Solution().maxIncreasingSubarrays(nums = [1,3,2,4,5,6,7,8,9,10]) == 4

assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,4,4,4,5,6,7]) == 2

assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,1]) == 4

assert Solution().maxIncreasingSubarrays(nums = [1,2,3,2,1,2,3,4,5,6]) == 3

assert Solution().maxIncreasingSubarrays(nums = [1,3,5,4,6,7,8,2,3,4,5,6,7]) == 4

assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,1,2,3,4,5]) == 5

assert Solution().maxIncreasingSubarrays(nums = [1,1,2,2,3,3,4,4,5,5]) == 2

assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,1,2,3,4]) == 4

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,3,2,4,3,5,4,6,5,7]) == 2

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,3,5,7,9,11,13,15]) == 4

Answer: assert Solution().maxIncreasingSubarrays(nums = [10,20,30,25,35,45,55,65,75]) == 3

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,2,3,4,5,6,7,8,9]) == 4

Answer: assert Solution().maxIncreasingSubarrays(nums = [2,5,7,8,9,2,3,4,3,1]) == 3

Answer: assert Solution().maxIncreasingSubarrays(nums = [10,9,8,7,6,5,4,3,2,1]) == 1

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,1,2,3,1,2,3,1]) == 3

Answer: assert Solution().maxIncreasingSubarrays(nums = [20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1]) == 1

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,2,3,4,5,4,5,6]) == 3

Answer: assert Solution().maxIncreasingSubarrays(nums = [5,6,7,8,9,10,11,12,13,14,15]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,3,5,7,9,11,13,15,17,19]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,3,5,7,9,2,4,6,8,10]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,3,4,5,6,7]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [5,6,7,8,9,1,2,3,4,5,6,7,8,9,10]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,1,1,1,1,1,1,1,1,1]) == 1

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,1,2,1,2,1,2,1,2]) == 2

Answer: assert Solution().maxIncreasingSubarrays(nums = [9,8,7,6,5,4,3,2,1,2,3,4,5,6,7,8,9]) == 4

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,3,2,4,5,6,7,8,9,10]) == 4

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,1,2,3,4,5]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,4,4,4,5,6,7]) == 2

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,1]) == 4

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]) == 7

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,2,3,4,5,6,7,8,9,10,11]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 7

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,3,5,7,9,2,4,6,8,10,1,2,3,4,5]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,10,2,9,3,8,4,7,5,6,11,20,12,19,13,18,14,17,15,16]) == 2

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 3, 5, 7, 9, 8, 10, 12, 14, 13, 15, 17, 19]) == 4

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 10, 2, 9, 3, 8, 4, 7, 5, 6, 11, 20, 12, 19, 13, 18, 14, 17, 15, 16, 21, 30, 22, 29, 23, 28, 24, 27, 25, 26]) == 2

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31]) == 8

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,2,1,2,3,4,5,6]) == 3

Answer: assert Solution().maxIncreasingSubarrays(nums = [5,4,3,2,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,1,2,3,4,5,6,7,8,9,10]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,3,5,7,9,2,4,6,8,10,3,5,7,9,11,4,6,8,10,12]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [2, 4, 6, 8, 10, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 1, 3, 5, 7]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]) == 7

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,3,5,4,6,7,8,2,3,4,5,6,7]) == 4

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 3, 2, 4, 6, 5, 7, 9, 8, 10, 12, 11, 13, 15, 14, 16, 18, 17, 19, 21, 20, 22, 24, 23, 25, 27, 26, 28, 30]) == 3

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,2,3,4,3,4,5,4,5,6,5,6,7,6,7,8,7,8,9]) == 3

Answer: assert Solution().maxIncreasingSubarrays(nums = [9,8,7,6,5,4,3,2,1,10,11,12,13,14,15,16,17,18,19,20]) == 6

Answer: assert Solution().maxIncreasingSubarrays(nums = [5,4,3,2,1,6,7,8,9,10,5,4,3,2,1,6,7,8,9,10,5,4,3,2,1,6,7,8,9,10]) == 3

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,2,3,4,5,6,7,8,9,10]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,9,8,7,6,5,4,3,2,1,1,2,3,4,5,6,7,8,9,10,2,3]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 9

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,3,5,7,9,2,4,6,8,10,1,3,5,7,9,2,4,6,8,10]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,1,2,3,4,5]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [5,6,7,8,9,10,11,12,13,14,15,1,2,3,4]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [9,8,7,6,5,4,3,2,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]) == 12

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,9,8,7,6,5,4,3,2,1]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]) == 15

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59]) == 15

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,1,1,1,1,1,1,1,1,1,2,3,4,5,6,7,8,9,10,11,12]) == 6

Answer: assert Solution().maxIncreasingSubarrays(nums = [9,8,7,6,5,4,3,2,1,0,9,8,7,6,5,4,3,2,1]) == 1

Answer: assert Solution().maxIncreasingSubarrays(nums = [30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 1

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49]) == 12

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,1,3,5,7,9,11,13,15,17,19,1,2,3,4,5,6,7,8,9,10]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,9,8,7,6,5,4,3,2,1,0,1,2,3,4]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,9,8,7,6,5,4,3,2,1,2,3,4,5,6,7,8,9,10]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,1,2,3,4,5,6,7,8,9,10]) == 9

Answer: assert Solution().maxIncreasingSubarrays(nums = [10,20,30,40,50,60,70,80,90,100,10,20,30,40,50]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 9

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,3,2,4,3,5,4,6,5,7,4,5,6,7,8,5,6,7,8,9,6,7,8,9,10]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [31,29,27,25,23,21,19,17,15,13,11,9,7,5,3,1]) == 1

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 20

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,9,8,7,6,5,4,3,2,1,1,2,3,4,5,6,7,8,9,10,2,3,4,5]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [100, 200, 300, 250, 260, 270, 280, 290, 300, 200, 210, 220, 230, 240, 250]) == 6

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,5,6,7,8,9,10,11,12,13,14]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [10,20,30,40,35,45,55,65,75,85,95,105]) == 4

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,2,3]) == 7

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2]) == 2

Answer: assert Solution().maxIncreasingSubarrays(nums = [5,4,3,2,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]) == 8

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,1,2,2,3,3,4,4,5,5]) == 2

Answer: assert Solution().maxIncreasingSubarrays(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10]) == 2

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,2,3,4,5,6,7,8,9,10,1]) == 9

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 5, 6, 7, 8, 9, 10, 15, 16, 17, 18, 19, 20]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [5,6,7,8,9,10,1,2,3,4,5,6,7,8,9]) == 6

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 20

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 3, 2, 4, 6, 5, 7, 9, 8, 10, 12, 11, 13, 15, 14, 16, 18, 17, 19, 21, 20, 22, 24, 23, 25, 27, 26, 28, 30, 29, 31, 33, 32, 34, 36, 35, 37, 39, 38, 40]) == 3

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,1,2,3,4]) == 4

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,1,2,3,4,5,6,7,8,9,10,1,2,3,4,5]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3]) == 3

Answer: assert Solution().maxIncreasingSubarrays(nums = [2,3,5,6,8,9,11,12,14,15,17,18,20,21,23,24,26,27,29,30,1,3,5,7,9,11,13,15,17,19]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,2,3,4,5,6,7,8,9,10]) == 9

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2]) == 2

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]) == 21

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,1,2,3,4,5,6,7,8,9,10]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,1,2,3,4,5,6,7,8,9,10]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 3, 5, 7, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 6

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 15

Answer: assert Solution().maxIncreasingSubarrays(nums = [10,9,8,7,6,5,4,3,2,1,10,9,8,7,6,5,4,3,2,1]) == 1

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,2,1,4,5,4,3,2,1,6,7,8,9,8,7,6,5,4]) == 2

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1]) == 1

Answer: assert Solution().maxIncreasingSubarrays(nums = [100,200,300,250,350,450,550,400,500,600,700,800,900]) == 4

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25]) == 12

Answer: assert Solution().maxIncreasingSubarrays(nums = [10,20,30,40,50,60,70,80,90,100]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,9,8,7,6,5,4,3,2,1,1,2,3,4,5,6,7,8,9,10,1]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [100, 200, 300, 400, 500, 450, 550, 650, 750, 850, 950, 1050, 900, 1000, 1100, 1200, 1300]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,9,8,7,6,5,4,3,2,1,1,2,3,4,5,6,7,8,9,10,2,3,4]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,1,3,5,7,9,11,13,15,17,19]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79]) == 20

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10]) == 9

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5]) == 9

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,10,2,9,3,8,4,7,5,6,1,10,2,9,3,8,4,7,5,6]) == 2

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2]) == 2

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3]) == 1

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [10,20,30,25,35,45,55,40,50,60,70,80,90,100,110]) == 4

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,9,8,7,6,5,4,3,2,1,1,2,3,4,5,6,7,8,9,10]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9]) == 9

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [10,9,8,7,6,5,4,3,2,1,10,9,8,7,6,5,4,3,2,1,10,9,8,7,6]) == 1

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,9,8,7,6,5,4,3,2,1,10,9,8,7,6,5,4,3,2,1]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,2,1,2,3,2,1,2,3,2,1,2,3,2,1,2,3,2,1,2,3,2,1,2,3,2,1]) == 1

Answer: assert Solution().maxIncreasingSubarrays(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]) == 8

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,3,5,7,9,11,13,15,17,19,1,3,5,7,9,11,13,15,17,19]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 3, 5, 7, 9, 11, 10, 12, 14, 16, 18, 20, 19, 21, 23, 25]) == 6

Answer: assert Solution().maxIncreasingSubarrays(nums = [10, 20, 30, 40, 50, 45, 46, 47, 48, 49, 50, 55, 60, 65, 70]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4]) == 8

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 8

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,1,2,3,4,5,6,7,8,9,10,6,7,8,9,10,11,12,13,14,15]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,100,2,99,3,98,4,97,5,96,6,95,7,94,8,93,9,92,10,91]) == 2

Answer: assert Solution().maxIncreasingSubarrays(nums = [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]) == 8

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 10

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]) == 8

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5]) == 2

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]) == 11

Answer: assert Solution().maxIncreasingSubarrays(nums = [100,99,98,97,96,95,94,93,92,91,1,2,3,4,5,6,7,8,9,10]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5]) == 5

Answer: assert Solution().maxIncreasingSubarrays(nums = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6]) == 9

Answer: assert Solution().maxIncreasingSubarrays(nums = [1,2,3,2,1,4,5,6,5,4,7,8,9,8,7,10,11,12,11,10]) == 2

Answer: assert Solution().maxIncreasingSubarrays(nums = [1, 3, 5, 7, 9, 11, 13, 15, 1, 3, 5, 7, 9, 11, 13, 15, 1, 3, 5, 7, 9]) == 8

import random
import functools
import collections
import string
import math
import datetime

from typing import *
from functools import *
from collections import *
from itertools import *
from heapq import *
from bisect import *
from string import *
from operator import *
from math import *

inf = float('inf')

class ListNode:
    def __init__(self, val=0, next=None):
        self.val = val
        self.next = next

def list_node(values: list):
    if not values:
        return None
    head = ListNode(values[0])
    p = head
    for val in values[1:]:
        node = ListNode(val)
        p.next = node
        p = node
    return head

def is_same_list(p1, p2):
    if p1 is None and p2 is None:
        return True
    if not p1 or not p2:
        return False
    return p1.val == p2.val and is_same_list(p1.next, p2.next)

class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def tree_node(values: list):
    if not values:
        return None
    root = TreeNode(values[0])
    i = 1
    queue = deque()
    queue.append(root)
    while queue:
        node = queue.popleft()
        if i < len(values) and values[i] is not None:
            node.left = TreeNode(values[i])
            queue.append(node.left)
        i += 1
        if i < len(values) and values[i] is not None:
            node.right = TreeNode(values[i])
            queue.append(node.right)
        i += 1
    return root

def is_same_tree(p, q):
    if not p and not q:
        return True
    elif not p or not q:
        return False
    elif p.val != q.val:
        return False
    else:
        return is_same_tree(p.left, q.left) and is_same_tree(p.right, q.right)

class Solution:
    def maxIncreasingSubarrays(self, nums: List[int]) -> int:
        ans = pre = cur = 0
        for i, x in enumerate(nums):
            cur += 1
            if i == len(nums) - 1 or x >= nums[i + 1]:
                ans = max(ans, cur // 2, min(pre, cur))
                pre, cur = cur, 0
        return ans


You are an expert Python programmer. Write correct, efficient Python 3 code that solves the problem and passes all tests. Output the code in the following format: ```python
<code>
```

PROBLEM:
You are given an integer array nums. A good subsequence is defined as a subsequence of nums where the absolute difference between any two consecutive elements in the subsequence is exactly 1.
Return the sum of all possible good subsequences of nums.
Since the answer may be very large, return it modulo 109 + 7.
Note that a subsequence of size 1 is considered good by definition.

Example 1:

Input: nums = [1,2,1]
Output: 14
Explanation:

Good subsequences are: [1], [2], [1], [1,2], [2,1], [1,2,1].
The sum of elements in these subsequences is 14.

Example 2:

Input: nums = [3,4,5]
Output: 40
Explanation:

Good subsequences are: [3], [4], [5], [3,4], [4,5], [3,4,5].
The sum of elements in these subsequences is 40.

Constraints:

1 <= nums.length <= 105
0 <= nums[i] <= 105

Your solution to the problem should be a method of the class Solution called sumOfGoodSubsequences and should pass all tests. Use the following starter code:
```python
class Solution:
    def sumOfGoodSubsequences(self, nums: List[int]) -> int:
        # Add your code here
```

SOLUTION:

Question:
PROBLEM:
You are given an integer array nums. A good subsequence is defined as a subsequence of nums where the absolute difference between any two consecutive elements in the subsequence is exactly 1.
Return the sum of all possible good subsequences of nums.
Since the answer may be very large, return it modulo 109 + 7.
Note that a subsequence of size 1 is considered good by definition.

Example 1:

Input: nums = [1,2,1]
Output: 14
Explanation:

Good subsequences are: [1], [2], [1], [1,2], [2,1], [1,2,1].
The sum of elements in these subsequences is 14.

Example 2:

Input: nums = [3,4,5]
Output: 40
Explanation:

Good subsequences are: [3], [4], [5], [3,4], [4,5], [3,4,5].
The sum of elements in these subsequences is 40.

Constraints:

1 <= nums.length <= 105
0 <= nums[i] <= 105

Your solution to the problem should be a method of the class Solution called sumOfGoodSubsequences and should pass all tests. Use the following starter code:
```python
class Solution:
    def sumOfGoodSubsequences(self, nums: List[int]) -> int:
        # Add your code here
```

SOLUTION:

assert Solution().sumOfGoodSubsequences(nums = [5,5,5,6,6,7,7,8,8,9,9]) == 3681

assert Solution().sumOfGoodSubsequences(nums = [0,1,2,3,4,5]) == 140

assert Solution().sumOfGoodSubsequences(nums = [0,0,0,0,0,0,0,0,0,0]) == 0

assert Solution().sumOfGoodSubsequences(nums = [0,1,2,3,4,5,6,7,8,9,10]) == 1430

assert Solution().sumOfGoodSubsequences(nums = [2,2,2,2,2,2,2,2,2,2]) == 20

assert Solution().sumOfGoodSubsequences(nums = [1,1,1,1]) == 4

assert Solution().sumOfGoodSubsequences(nums = [10,9,8,7,6,5,4,3,2,1]) == 1210

assert Solution().sumOfGoodSubsequences(nums = [1,3,5,7,9]) == 25

assert Solution().sumOfGoodSubsequences(nums = [1,3,5,7,9,10,8,6,4,2]) == 154

assert Solution().sumOfGoodSubsequences(nums = [3,4,5]) == 40

assert Solution().sumOfGoodSubsequences(nums = [1,1,2,2,3,3,4,4,5,5]) == 1206

assert Solution().sumOfGoodSubsequences(nums = [5,5,5,5,5]) == 25

assert Solution().sumOfGoodSubsequences(nums = [100000,99999,100001]) == 700000

assert Solution().sumOfGoodSubsequences(nums = [1,2,1]) == 14

assert Solution().sumOfGoodSubsequences(nums = [0,0,0,0,0]) == 0

assert Solution().sumOfGoodSubsequences(nums = [1,3,5,7,9,11,13,15,17,19]) == 100

assert Solution().sumOfGoodSubsequences(nums = [0,0,0]) == 0

assert Solution().sumOfGoodSubsequences(nums = [1,1,1,1,1]) == 5

assert Solution().sumOfGoodSubsequences(nums = [2,2,2,3,3,4,4,4,5,5,6,6,6]) == 4132

assert Solution().sumOfGoodSubsequences(nums = [5,4,3,2,1]) == 105

assert Solution().sumOfGoodSubsequences(nums = [5,4,3,2,1,0]) == 140

assert Solution().sumOfGoodSubsequences(nums = [1,2,3,2,1]) == 83

assert Solution().sumOfGoodSubsequences(nums = [0,0,0,1,1,1,2,2,2]) == 126

assert Solution().sumOfGoodSubsequences(nums = [1, 2, 3, 2, 3, 4, 3, 4, 5]) == 1566

assert Solution().sumOfGoodSubsequences(nums = [1,2,3,4,5,6,7,8,9,10]) == 1210

assert Solution().sumOfGoodSubsequences(nums = [1, 3, 2, 5, 4, 7, 6, 9, 8, 10]) == 154

assert Solution().sumOfGoodSubsequences(nums = [10, 9, 10, 8, 9, 10, 7, 8, 9, 10]) == 4192

assert Solution().sumOfGoodSubsequences(nums = [5, 6, 7, 8, 9, 10, 5, 6, 7, 8, 9, 10]) == 4515

assert Solution().sumOfGoodSubsequences(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5]) == 1206

assert Solution().sumOfGoodSubsequences(nums = [1,2,3,2,1,2,3,2,1]) == 1084

assert Solution().sumOfGoodSubsequences(nums = [1, 2, 1, 3, 2, 4, 3, 5, 4, 6]) == 646

assert Solution().sumOfGoodSubsequences(nums = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 1608

assert Solution().sumOfGoodSubsequences(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 1210

assert Solution().sumOfGoodSubsequences(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == 100

assert Solution().sumOfGoodSubsequences(nums = [0, 1, 0, 2, 0, 3, 0, 4, 0, 5]) == 148

assert Solution().sumOfGoodSubsequences(nums = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7]) == 600

assert Solution().sumOfGoodSubsequences(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 1210

assert Solution().sumOfGoodSubsequences(nums = [2, 4, 2, 4, 2, 4, 2, 4, 2, 4]) == 30

assert Solution().sumOfGoodSubsequences(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 1430

assert Solution().sumOfGoodSubsequences(nums = [10, 9, 10, 9, 10, 9, 10, 9, 10]) == 5394

assert Solution().sumOfGoodSubsequences(nums = [1, 10, 2, 9, 3, 8, 4, 7, 5, 6]) == 470

assert Solution().sumOfGoodSubsequences(nums = [1, 2, 2, 3, 3, 3, 4, 4, 5]) == 807

assert Solution().sumOfGoodSubsequences(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 10

assert Solution().sumOfGoodSubsequences(nums = [5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5]) == 0

assert Solution().sumOfGoodSubsequences(nums = [1, 2, 2, 3, 3, 3, 4]) == 225

assert Solution().sumOfGoodSubsequences(nums = [10, 9, 10, 11, 12, 11, 10, 9, 8, 7]) == 5234

Answer: assert Solution().sumOfGoodSubsequences(nums = [5,5,5,6,6,7,7,8,8,9,9]) == 3681

Answer: assert Solution().sumOfGoodSubsequences(nums = [0,1,2,3,4,5]) == 140

Answer: assert Solution().sumOfGoodSubsequences(nums = [0,0,0,0,0,0,0,0,0,0]) == 0

Answer: assert Solution().sumOfGoodSubsequences(nums = [0,1,2,3,4,5,6,7,8,9,10]) == 1430

Answer: assert Solution().sumOfGoodSubsequences(nums = [2,2,2,2,2,2,2,2,2,2]) == 20

Answer: assert Solution().sumOfGoodSubsequences(nums = [1,1,1,1]) == 4

Answer: assert Solution().sumOfGoodSubsequences(nums = [10,9,8,7,6,5,4,3,2,1]) == 1210

Answer: assert Solution().sumOfGoodSubsequences(nums = [1,3,5,7,9]) == 25

Answer: assert Solution().sumOfGoodSubsequences(nums = [1,3,5,7,9,10,8,6,4,2]) == 154

Answer: assert Solution().sumOfGoodSubsequences(nums = [3,4,5]) == 40

Answer: assert Solution().sumOfGoodSubsequences(nums = [1,1,2,2,3,3,4,4,5,5]) == 1206

Answer: assert Solution().sumOfGoodSubsequences(nums = [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]) == 100

Answer: assert Solution().sumOfGoodSubsequences(nums = [5,5,5,5,5]) == 25

Answer: assert Solution().sumOfGoodSubsequences(nums = [100000,99999,100000,99999]) == 2199989

Answer: assert Solution().sumOfGoodSubsequences(nums = [100000,99999,100001]) == 700000

Answer: assert Solution().sumOfGoodSubsequences(nums = [1,2,1]) == 14

Answer: assert Solution().sumOfGoodSubsequences(nums = [0,0,0,0,0]) == 0

Answer: assert Solution().sumOfGoodSubsequences(nums = [1,3,5,7,9,11,13,15,17,19]) == 100

Answer: assert Solution().sumOfGoodSubsequences(nums = [0,0,0]) == 0

Answer: assert Solution().sumOfGoodSubsequences(nums = [1,1,1,1,1]) == 5

Answer: assert Solution().sumOfGoodSubsequences(nums = [100000, 99999, 100000, 99998, 99999, 100000]) == 7199950

Answer: assert Solution().sumOfGoodSubsequences(nums = [100000,99999,99998,99997]) == 1999970

Answer: assert Solution().sumOfGoodSubsequences(nums = [2,2,2,3,3,4,4,4,5,5,6,6,6]) == 4132

Answer: assert Solution().sumOfGoodSubsequences(nums = [5,4,3,2,1]) == 105

Answer: assert Solution().sumOfGoodSubsequences(nums = [5,4,3,2,1,0]) == 140

Answer: assert Solution().sumOfGoodSubsequences(nums = [1,2,3,2,1]) == 83

Answer: assert Solution().sumOfGoodSubsequences(nums = [0,0,0,1,1,1,2,2,2]) == 126

Answer: assert Solution().sumOfGoodSubsequences(nums = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]) == 16170

Answer: assert Solution().sumOfGoodSubsequences(nums = [100000,99999,99998,99997,99996]) == 3499930

Answer: assert Solution().sumOfGoodSubsequences(nums = [100, 101, 100, 102, 101, 103, 102, 104, 103, 105]) == 23020

Answer: assert Solution().sumOfGoodSubsequences(nums = [10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9]) == 2409295

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 2, 3, 2, 3, 4, 3, 4, 5]) == 1566

Answer: assert Solution().sumOfGoodSubsequences(nums = [50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20]) == 190960

Answer: assert Solution().sumOfGoodSubsequences(nums = [1,2,3,4,5,6,7,8,9,10,9,8,7,6,5,4,3,2,1,2]) == 35876

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 2, 3, 2, 3, 4, 3, 4, 5, 4, 5, 6, 5, 6, 7]) == 52520

Answer: assert Solution().sumOfGoodSubsequences(nums = [1,2,3,4,5,6,7,8,9,10]) == 1210

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 380415

Answer: assert Solution().sumOfGoodSubsequences(nums = [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]) == 22330

Answer: assert Solution().sumOfGoodSubsequences(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 16170

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 3, 2, 4, 5, 3, 4, 5, 6, 7, 8, 9, 10]) == 3640

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 62

Answer: assert Solution().sumOfGoodSubsequences(nums = [5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6]) == 1394855

Answer: assert Solution().sumOfGoodSubsequences(nums = [5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4]) == 1141245

Answer: assert Solution().sumOfGoodSubsequences(nums = [3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2]) == 504965

Answer: assert Solution().sumOfGoodSubsequences(nums = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]) == 20

Answer: assert Solution().sumOfGoodSubsequences(nums = [1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1]) == 2072577

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 3, 2, 5, 4, 7, 6, 9, 8, 10]) == 154

Answer: assert Solution().sumOfGoodSubsequences(nums = [100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000]) == 800000

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10]) == 4400

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33]) == 289

Answer: assert Solution().sumOfGoodSubsequences(nums = [10, 9, 10, 8, 9, 10, 7, 8, 9, 10]) == 4192

Answer: assert Solution().sumOfGoodSubsequences(nums = [5, 6, 7, 8, 9, 10, 5, 6, 7, 8, 9, 10]) == 4515

Answer: assert Solution().sumOfGoodSubsequences(nums = [1,3,2,4,3,5,4,6,5,7,6,8,7,9,8,10]) == 4400

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 39653471

Answer: assert Solution().sumOfGoodSubsequences(nums = [100, 99, 101, 98, 102, 97, 103, 96, 104, 95, 105]) == 11100

Answer: assert Solution().sumOfGoodSubsequences(nums = [1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,7]) == 406268

Answer: assert Solution().sumOfGoodSubsequences(nums = [10, 9, 10, 11, 10, 9, 10, 11, 10, 9, 10]) == 18005

Answer: assert Solution().sumOfGoodSubsequences(nums = [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 4290

Answer: assert Solution().sumOfGoodSubsequences(nums = [50000, 49999, 50000, 49998, 49999, 50000, 50001, 50002, 50001, 50000]) == 32350024

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == 180378

Answer: assert Solution().sumOfGoodSubsequences(nums = [100000, 99999, 99998, 99997, 99996, 99995, 99994, 99993, 99992, 99991]) == 21999010

Answer: assert Solution().sumOfGoodSubsequences(nums = [50000, 49999, 50001, 49998, 50000, 49999, 50002, 49999, 50001, 50000]) == 11949964

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2]) == 509475

Answer: assert Solution().sumOfGoodSubsequences(nums = [50, 51, 52, 53, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20]) == 822512

Answer: assert Solution().sumOfGoodSubsequences(nums = [1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10]) == 180378

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5]) == 1206

Answer: assert Solution().sumOfGoodSubsequences(nums = [100000, 99999, 100000, 99998, 99999, 100000, 99997, 99998, 99999, 100000]) == 46199572

Answer: assert Solution().sumOfGoodSubsequences(nums = [1,2,3,4,5,4,3,2,1,2,3,4,5,4,3,2,1,2,3,4]) == 201606

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6]) == 1503158

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]) == 38025

Answer: assert Solution().sumOfGoodSubsequences(nums = [1,2,3,2,1,2,3,2,1]) == 1084

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10]) == 7966

Answer: assert Solution().sumOfGoodSubsequences(nums = [100000, 99999, 99998, 99997, 99996, 99995, 99994, 99993, 99992, 99991, 99990, 99989, 99988, 99987, 99986, 99985, 99984, 99983, 99982, 99981]) == 153985370

Answer: assert Solution().sumOfGoodSubsequences(nums = [1,2,2,3,3,3,4,4,4,4,5,5,5,5,5]) == 5047

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 2, 1, 3, 2, 4, 3, 5, 4, 6]) == 646

Answer: assert Solution().sumOfGoodSubsequences(nums = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 1608

Answer: assert Solution().sumOfGoodSubsequences(nums = [50000, 50001, 49999, 50002, 50003, 49998, 50004]) == 2200060

Answer: assert Solution().sumOfGoodSubsequences(nums = [100, 99, 101, 100, 102, 101, 103, 102, 104, 103]) == 24360

Answer: assert Solution().sumOfGoodSubsequences(nums = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 126805

Answer: assert Solution().sumOfGoodSubsequences(nums = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]) == 22330

Answer: assert Solution().sumOfGoodSubsequences(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 1210

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == 100

Answer: assert Solution().sumOfGoodSubsequences(nums = [0, 1, 0, 2, 0, 3, 0, 4, 0, 5]) == 148

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7]) == 600

Answer: assert Solution().sumOfGoodSubsequences(nums = [1,10,1,10,1,10,1,10,1,10,1,10,1,10,1,10,1,10,1,10,1,10,1,10,1,10,1,10,1,10]) == 165

Answer: assert Solution().sumOfGoodSubsequences(nums = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 14761

Answer: assert Solution().sumOfGoodSubsequences(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 37356

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 1210

Answer: assert Solution().sumOfGoodSubsequences(nums = [1,2,1,3,2,4,3,5,4,6,5,7,6,8,7,9,8,10,9,11,10,12,11,13,12,14,13,15,14,16,15,17,16,18,17,19,18,20]) == 256881

Answer: assert Solution().sumOfGoodSubsequences(nums = [2, 4, 2, 4, 2, 4, 2, 4, 2, 4]) == 30

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1]) == 118724

Answer: assert Solution().sumOfGoodSubsequences(nums = [5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5]) == 49362

Answer: assert Solution().sumOfGoodSubsequences(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 1430

Answer: assert Solution().sumOfGoodSubsequences(nums = [10, 9, 10, 9, 10, 9, 10, 9, 10]) == 5394

Answer: assert Solution().sumOfGoodSubsequences(nums = [50000, 49999, 50000, 49998, 49999, 50000, 49997, 49998, 49999, 50000]) == 23099572

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 10, 2, 9, 3, 8, 4, 7, 5, 6]) == 470

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 16170

Answer: assert Solution().sumOfGoodSubsequences(nums = [7, 8, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 8766

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 2, 2, 3, 3, 3, 4, 4, 5]) == 807

Answer: assert Solution().sumOfGoodSubsequences(nums = [1,10,2,9,3,8,4,7,5,6,1,10,2,9,3,8,4,7,5,6]) == 5341

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 10

Answer: assert Solution().sumOfGoodSubsequences(nums = [7, 8, 7, 9, 10, 8, 9, 10, 11, 12, 11, 12, 13]) == 17923

Answer: assert Solution().sumOfGoodSubsequences(nums = [0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 12, 0, 13, 0, 14, 0, 15, 0, 16, 0, 17, 0, 18, 0, 19, 0, 20]) == 17748

Answer: assert Solution().sumOfGoodSubsequences(nums = [50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60]) == 15730

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 603306

Answer: assert Solution().sumOfGoodSubsequences(nums = [5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5]) == 0

Answer: assert Solution().sumOfGoodSubsequences(nums = [50000, 50001, 50000, 50001, 50000, 50001, 50000, 50001]) == 15500155

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 2, 2, 3, 3, 3, 4]) == 225

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3]) == 81712

Answer: assert Solution().sumOfGoodSubsequences(nums = [50000, 50001, 50002, 50003, 50004, 50005, 50006, 50007, 50008, 50009]) == 11000990

Answer: assert Solution().sumOfGoodSubsequences(nums = [100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000]) == 1000000

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5]) == 19722

Answer: assert Solution().sumOfGoodSubsequences(nums = [1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2]) == 380415

Answer: assert Solution().sumOfGoodSubsequences(nums = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115]) == 87720

Answer: assert Solution().sumOfGoodSubsequences(nums = [100000, 99999, 99998, 99997, 99996, 99995, 99994, 99993, 99992, 99991, 100000, 99999, 99998]) == 29598920

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14, 17, 16, 19, 18, 21, 20, 23, 22, 25, 24, 27, 26, 29, 28, 31, 30]) == 1456

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 2, 3, 4, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5]) == 1552

Answer: assert Solution().sumOfGoodSubsequences(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 20

Answer: assert Solution().sumOfGoodSubsequences(nums = [2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 652102

Answer: assert Solution().sumOfGoodSubsequences(nums = [100000, 99999, 99998, 99997, 99996, 99995, 99994, 99993, 99992, 99991, 99990, 99989, 99988, 99987, 99986, 99985, 99984, 99983, 99982, 99981, 99980, 99979, 99978, 99977, 99976, 99975, 99974, 99973, 99972, 99971, 99970]) == 545518160

Answer: assert Solution().sumOfGoodSubsequences(nums = [10, 9, 10, 11, 12, 11, 10, 9, 8, 7]) == 5234

Answer: assert Solution().sumOfGoodSubsequences(nums = [50000, 49999, 50001, 49998, 50002, 49997, 50003, 49996, 50004, 49995]) == 4499930

Answer: assert Solution().sumOfGoodSubsequences(nums = [100000, 99999, 100000, 99998, 99999, 100000, 99997, 99998, 99999]) == 26199726

Answer: assert Solution().sumOfGoodSubsequences(nums = [10, 9, 10, 11, 10, 12, 11, 13, 12, 14, 13, 15, 14, 16, 15, 17, 16, 18]) == 30424

import random
import functools
import collections
import string
import math
import datetime

from typing import *
from functools import *
from collections import *
from itertools import *
from heapq import *
from bisect import *
from string import *
from operator import *
from math import *

inf = float('inf')

class ListNode:
    def __init__(self, val=0, next=None):
        self.val = val
        self.next = next

def list_node(values: list):
    if not values:
        return None
    head = ListNode(values[0])
    p = head
    for val in values[1:]:
        node = ListNode(val)
        p.next = node
        p = node
    return head

def is_same_list(p1, p2):
    if p1 is None and p2 is None:
        return True
    if not p1 or not p2:
        return False
    return p1.val == p2.val and is_same_list(p1.next, p2.next)

class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def tree_node(values: list):
    if not values:
        return None
    root = TreeNode(values[0])
    i = 1
    queue = deque()
    queue.append(root)
    while queue:
        node = queue.popleft()
        if i < len(values) and values[i] is not None:
            node.left = TreeNode(values[i])
            queue.append(node.left)
        i += 1
        if i < len(values) and values[i] is not None:
            node.right = TreeNode(values[i])
            queue.append(node.right)
        i += 1
    return root

def is_same_tree(p, q):
    if not p and not q:
        return True
    elif not p or not q:
        return False
    elif p.val != q.val:
        return False
    else:
        return is_same_tree(p.left, q.left) and is_same_tree(p.right, q.right)

class Solution:
    def sumOfGoodSubsequences(self, nums: List[int]) -> int:
        mod = 10**9 + 7
        f = defaultdict(int)
        g = defaultdict(int)
        for x in nums:
            f[x] += x
            g[x] += 1
            f[x] += f[x - 1] + g[x - 1] * x
            g[x] += g[x - 1]
            f[x] += f[x + 1] + g[x + 1] * x
            g[x] += g[x + 1]
        return sum(f.values()) % mod


You are an expert Python programmer. Write correct, efficient Python 3 code that solves the problem and passes all tests. Output the code in the following format: ```python
<code>
```

PROBLEM:
You are given a binary string s representing a number n in its binary form.
You are also given an integer k.
An integer x is called k-reducible if performing the following operation at most k times reduces it to 1:

Replace x with the count of set bits in its binary representation.

For example, the binary representation of 6 is "110". Applying the operation once reduces it to 2 (since "110" has two set bits). Applying the operation again to 2 (binary "10") reduces it to 1 (since "10" has one set bit).
Return an integer denoting the number of positive integers less than n that are k-reducible.
Since the answer may be too large, return it modulo 109 + 7.

Example 1:

Input: s = "111", k = 1
Output: 3
Explanation:
n = 7. The 1-reducible integers less than 7 are 1, 2, and 4.

Example 2:

Input: s = "1000", k = 2
Output: 6
Explanation:
n = 8. The 2-reducible integers less than 8 are 1, 2, 3, 4, 5, and 6.

Example 3:

Input: s = "1", k = 3
Output: 0
Explanation:
There are no positive integers less than n = 1, so the answer is 0.

Constraints:

1 <= s.length <= 800
s has no leading zeros.
s consists only of the characters '0' and '1'.
1 <= k <= 5

Your solution to the problem should be a method of the class Solution called countKReducibleNumbers and should pass all tests. Use the following starter code:
```python
class Solution:
    def countKReducibleNumbers(self, s: str, k: int) -> int:
        # Add your code here
```

SOLUTION:

Question:
PROBLEM:
You are given a binary string s representing a number n in its binary form.
You are also given an integer k.
An integer x is called k-reducible if performing the following operation at most k times reduces it to 1:

Replace x with the count of set bits in its binary representation.

For example, the binary representation of 6 is "110". Applying the operation once reduces it to 2 (since "110" has two set bits). Applying the operation again to 2 (binary "10") reduces it to 1 (since "10" has one set bit).
Return an integer denoting the number of positive integers less than n that are k-reducible.
Since the answer may be too large, return it modulo 109 + 7.

Example 1:

Input: s = "111", k = 1
Output: 3
Explanation:
n = 7. The 1-reducible integers less than 7 are 1, 2, and 4.

Example 2:

Input: s = "1000", k = 2
Output: 6
Explanation:
n = 8. The 2-reducible integers less than 8 are 1, 2, 3, 4, 5, and 6.

Example 3:

Input: s = "1", k = 3
Output: 0
Explanation:
There are no positive integers less than n = 1, so the answer is 0.

Constraints:

1 <= s.length <= 800
s has no leading zeros.
s consists only of the characters '0' and '1'.
1 <= k <= 5

Your solution to the problem should be a method of the class Solution called countKReducibleNumbers and should pass all tests. Use the following starter code:
```python
class Solution:
    def countKReducibleNumbers(self, s: str, k: int) -> int:
        # Add your code here
```

SOLUTION:

assert Solution().countKReducibleNumbers(s = "1101101", k = 4) == 108

assert Solution().countKReducibleNumbers(s = "1100100", k = 3) == 99

assert Solution().countKReducibleNumbers(s = "11001100", k = 4) == 203

assert Solution().countKReducibleNumbers(s = "11111111", k = 5) == 254

assert Solution().countKReducibleNumbers(s = "1", k = 3) == 0

assert Solution().countKReducibleNumbers(s = "10000000", k = 5) == 127

assert Solution().countKReducibleNumbers(s = "101010", k = 3) == 41

assert Solution().countKReducibleNumbers(s = "111", k = 1) == 3

assert Solution().countKReducibleNumbers(s = "1000", k = 2) == 6

Answer: assert Solution().countKReducibleNumbers(s = "1101101", k = 4) == 108

Answer: assert Solution().countKReducibleNumbers(s = "1100100", k = 3) == 99

Answer: assert Solution().countKReducibleNumbers(s = "11001100", k = 4) == 203

Answer: assert Solution().countKReducibleNumbers(s = "11001001001001001001001001001001001001001001001001001001001001001", k = 4) == 343683436

Answer: assert Solution().countKReducibleNumbers(s = "111111111111111111111111111111111111111111111111111111111111111", k = 5) == 291172002

Answer: assert Solution().countKReducibleNumbers(s = "11111111", k = 5) == 254

Answer: assert Solution().countKReducibleNumbers(s = "1", k = 3) == 0

Answer: assert Solution().countKReducibleNumbers(s = "10000000", k = 5) == 127

Answer: assert Solution().countKReducibleNumbers(s = "101010", k = 3) == 41

Answer: assert Solution().countKReducibleNumbers(s = "111", k = 1) == 3

Answer: assert Solution().countKReducibleNumbers(s = "1111111111111111111111111111111111111111111111111111111111111111", k = 5) == 582344006

Answer: assert Solution().countKReducibleNumbers(s = "1000", k = 2) == 6

Answer: assert Solution().countKReducibleNumbers(s = "10101010101010101010101010101010101010101010101010101010101010101", k = 3) == 592177251

Answer: assert Solution().countKReducibleNumbers(s = "11010101010101010101010101010101010101010101010101010101010101010", k = 4) == 970573345

Answer: assert Solution().countKReducibleNumbers(s = "111100001111000011110000111100001111000011110000111100001111000011", k = 5) == 427648016

Answer: assert Solution().countKReducibleNumbers(s = "101101110111011101110111011101110111011101110111011101110111011101", k = 4) == 469386146

Answer: assert Solution().countKReducibleNumbers(s = "1000100010001000100010001000100010001000100010001000100010001000", k = 3) == 809688104

Answer: assert Solution().countKReducibleNumbers(s = "100010001000100010001000100010001000100010001000100010001000100010", k = 2) == 263516929

Answer: assert Solution().countKReducibleNumbers(s = "11111111111111111111111111111111111111111111111111111111111111111", k = 5) == 164688007

Answer: assert Solution().countKReducibleNumbers(s = "1111000011110000111100001111000011110000111100001111000011110000", k = 4) == 606912006

Answer: assert Solution().countKReducibleNumbers(s = "110101010101010101010101010101010101010101010101010101010101010101", k = 4) == 941146685

Answer: assert Solution().countKReducibleNumbers(s = "1010101010101010101010101010101010101010101010101010101010101010", k = 4) == 388229337

Answer: assert Solution().countKReducibleNumbers(s = "111010101010101010101010101010101010101010101010101010101010101", k = 3) == 802138855

Answer: assert Solution().countKReducibleNumbers(s = "110110110110110110110110110110110110110110110110110110110110110110", k = 4) == 568036587

Answer: assert Solution().countKReducibleNumbers(s = "11011011011011011011011011011011011011011011011011011011011011011", k = 3) == 67823251

Answer: assert Solution().countKReducibleNumbers(s = "11111111111111111111111111111111111111111111111111111111111111110", k = 2) == 720600285

Answer: assert Solution().countKReducibleNumbers(s = "1111111111111111111111111111111111111111111111111111111111111110", k = 5) == 582344005

Answer: assert Solution().countKReducibleNumbers(s = "10110110110110110110110110110110110110110110110110110110110110110", k = 5) == 403348578

Answer: assert Solution().countKReducibleNumbers(s = "1000000000000000000000000000000000000000000000000000000000000000", k = 5) == 291172003

Answer: assert Solution().countKReducibleNumbers(s = "10010010010010010010010010010010010010010010010010010010010010010", k = 4) == 522678864

Answer: assert Solution().countKReducibleNumbers(s = "111000111000111000111000111000111000111000111000111000111000111000", k = 5) == 70556457

Answer: assert Solution().countKReducibleNumbers(s = "11111111111111111111111111111111111111111111111111111111111111111", k = 3) == 158578985

Answer: assert Solution().countKReducibleNumbers(s = "101110111011101110111011101110111011101110111011101110111011101110", k = 5) == 108209077

Answer: assert Solution().countKReducibleNumbers(s = "1111100001111100001111100001111100001111100001111100001111100001", k = 5) == 306932732

Answer: assert Solution().countKReducibleNumbers(s = "100110011001100110011001100110011001100110011001100110011001100110", k = 3) == 207889528

Answer: assert Solution().countKReducibleNumbers(s = "10101010101010101010101010101010101010101010101010101010101010101", k = 5) == 776458676

Answer: assert Solution().countKReducibleNumbers(s = "1111100001111100001111100001111100001111100001111100001111100001111", k = 4) == 455461856

import random
import functools
import collections
import string
import math
import datetime

from typing import *
from functools import *
from collections import *
from itertools import *
from heapq import *
from bisect import *
from string import *
from operator import *
from math import *

inf = float('inf')

class ListNode:
    def __init__(self, val=0, next=None):
        self.val = val
        self.next = next

def list_node(values: list):
    if not values:
        return None
    head = ListNode(values[0])
    p = head
    for val in values[1:]:
        node = ListNode(val)
        p.next = node
        p = node
    return head

def is_same_list(p1, p2):
    if p1 is None and p2 is None:
        return True
    if not p1 or not p2:
        return False
    return p1.val == p2.val and is_same_list(p1.next, p2.next)

class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def tree_node(values: list):
    if not values:
        return None
    root = TreeNode(values[0])
    i = 1
    queue = deque()
    queue.append(root)
    while queue:
        node = queue.popleft()
        if i < len(values) and values[i] is not None:
            node.left = TreeNode(values[i])
            queue.append(node.left)
        i += 1
        if i < len(values) and values[i] is not None:
            node.right = TreeNode(values[i])
            queue.append(node.right)
        i += 1
    return root

def is_same_tree(p, q):
    if not p and not q:
        return True
    elif not p or not q:
        return False
    elif p.val != q.val:
        return False
    else:
        return is_same_tree(p.left, q.left) and is_same_tree(p.right, q.right)

class Solution:
  def countKReducibleNumbers(self, s: str, k: int) -> int:
    MOD = 1_000_000_007
    ops = self._getOps(s)

    @functools.lru_cache(None)
    def dp(i: int, setBits: int, tight: bool) -> int:
      """
      Returns the number of positive integers less than n that are k-reducible,
      considering the i-th digit, where `setBits` is the number of set bits in
      the current number, and `tight` indicates if the current digit is
      tightly bound.
      """
      if i == len(s):
        return int(ops[setBits] < k and not tight)

      res = 0
      maxDigit = int(s[i]) if tight else 1

      for d in range(maxDigit + 1):
        nextTight = tight and (d == maxDigit)
        res += dp(i + 1, setBits + d, nextTight)
        res %= MOD
      return res

    return dp(0, 0, True) - 1  # - 0

  def _getOps(self, s: str) -> int:
    """Returns the number of operations to reduce a number to 0."""
    ops = [0] * (len(s) + 1)
    for num in range(2, len(s) + 1):
      ops[num] = 1 + ops[num.bit_count()]
    return ops


You are an expert Python programmer. Write correct, efficient Python 3 code that solves the problem and passes all tests. Output the code in the following format: ```python
<code>
```

PROBLEM:
You are given an integer array nums of length n and a 2D array queries, where queries[i] = [li, ri].
For each queries[i]:

Select a subset of indices within the range [li, ri] in nums.
Decrement the values at the selected indices by 1.

A Zero Array is an array where all elements are equal to 0.
Return true if it is possible to transform nums into a Zero Array after processing all the queries sequentially, otherwise return false.

Example 1:

Input: nums = [1,0,1], queries = [[0,2]]
Output: true
Explanation:

For i = 0:

Select the subset of indices as [0, 2] and decrement the values at these indices by 1.
The array will become [0, 0, 0], which is a Zero Array.

Example 2:

Input: nums = [4,3,2,1], queries = [[1,3],[0,2]]
Output: false
Explanation:

For i = 0:

Select the subset of indices as [1, 2, 3] and decrement the values at these indices by 1.
The array will become [4, 2, 1, 0].

For i = 1:

Select the subset of indices as [0, 1, 2] and decrement the values at these indices by 1.
The array will become [3, 1, 0, 0], which is not a Zero Array.

Constraints:

1 <= nums.length <= 105
0 <= nums[i] <= 105
1 <= queries.length <= 105
queries[i].length == 2
0 <= li <= ri < nums.length

Your solution to the problem should be a method of the class Solution called isZeroArray and should pass all tests. Use the following starter code:
```python
class Solution:
    def isZeroArray(self, nums: List[int], queries: List[List[int]]) -> bool:
        # Add your code here
```

SOLUTION:

Question:
PROBLEM:
You are given an integer array nums of length n and a 2D array queries, where queries[i] = [li, ri].
For each queries[i]:

Select a subset of indices within the range [li, ri] in nums.
Decrement the values at the selected indices by 1.

A Zero Array is an array where all elements are equal to 0.
Return true if it is possible to transform nums into a Zero Array after processing all the queries sequentially, otherwise return false.

Example 1:

Input: nums = [1,0,1], queries = [[0,2]]
Output: true
Explanation:

For i = 0:

Select the subset of indices as [0, 2] and decrement the values at these indices by 1.
The array will become [0, 0, 0], which is a Zero Array.

Example 2:

Input: nums = [4,3,2,1], queries = [[1,3],[0,2]]
Output: false
Explanation:

For i = 0:

Select the subset of indices as [1, 2, 3] and decrement the values at these indices by 1.
The array will become [4, 2, 1, 0].

For i = 1:

Select the subset of indices as [0, 1, 2] and decrement the values at these indices by 1.
The array will become [3, 1, 0, 0], which is not a Zero Array.

Constraints:

1 <= nums.length <= 105
0 <= nums[i] <= 105
1 <= queries.length <= 105
queries[i].length == 2
0 <= li <= ri < nums.length

Your solution to the problem should be a method of the class Solution called isZeroArray and should pass all tests. Use the following starter code:
```python
class Solution:
    def isZeroArray(self, nums: List[int], queries: List[List[int]]) -> bool:
        # Add your code here
```

SOLUTION:

assert Solution().isZeroArray(nums = [0,0,0,0], queries = [[0,3],[1,2],[2,2]]) == True

assert Solution().isZeroArray(nums = [0,0,0,0], queries = [[0,3]]) == True

assert Solution().isZeroArray(nums = [5,4,3,2,1], queries = [[0,4],[1,3],[2,2]]) == False

assert Solution().isZeroArray(nums = [0,0,0,0], queries = [[0,3],[1,2],[2,3]]) == True

assert Solution().isZeroArray(nums = [1,0,1], queries = [[0,2]]) == True

assert Solution().isZeroArray(nums = [2,2,2], queries = [[0,2],[0,1],[1,2]]) == True

assert Solution().isZeroArray(nums = [2,2,2], queries = [[0,0],[1,1],[2,2]]) == False

assert Solution().isZeroArray(nums = [5,5,5,5,5], queries = [[0,2],[1,4],[0,3]]) == False

assert Solution().isZeroArray(nums = [3,3,3,3,3], queries = [[0,2],[1,3],[2,4]]) == False

assert Solution().isZeroArray(nums = [3,3,3], queries = [[0,2],[0,1],[1,2]]) == False

assert Solution().isZeroArray(nums = [2,2,2,2], queries = [[0,1],[2,3],[0,3]]) == True

assert Solution().isZeroArray(nums = [5,5,5,5], queries = [[0,3],[1,2],[2,3]]) == False

assert Solution().isZeroArray(nums = [3,3,3], queries = [[0,2],[0,2],[0,2]]) == True

assert Solution().isZeroArray(nums = [4,3,2,1], queries = [[1,3],[0,2]]) == False

Answer: assert Solution().isZeroArray(nums = [0,0,0,0], queries = [[0,3],[1,2],[2,2]]) == True

Answer: assert Solution().isZeroArray(nums = [0,0,0,0], queries = [[0,3]]) == True

Answer: assert Solution().isZeroArray(nums = [5,4,3,2,1], queries = [[0,4],[1,3],[2,2]]) == False

Answer: assert Solution().isZeroArray(nums = [0,0,0,0], queries = [[0,3],[1,2],[2,3]]) == True

Answer: assert Solution().isZeroArray(nums = [2,2,2,2,2], queries = [[0,4],[0,4],[0,4],[0,4],[0,4]]) == True

Answer: assert Solution().isZeroArray(nums = [1,0,1], queries = [[0,2]]) == True

Answer: assert Solution().isZeroArray(nums = [1,2,3,4,5], queries = [[0,1],[1,2],[2,3],[3,4]]) == False

Answer: assert Solution().isZeroArray(nums = [10,9,8,7,6,5,4,3,2,1], queries = [[0,9],[1,8],[2,7],[3,6],[4,5]]) == False

Answer: assert Solution().isZeroArray(nums = [2,2,2], queries = [[0,2],[0,1],[1,2]]) == True

Answer: assert Solution().isZeroArray(nums = [2,2,2], queries = [[0,0],[1,1],[2,2]]) == False

Answer: assert Solution().isZeroArray(nums = [5,5,5,5,5], queries = [[0,2],[1,4],[0,3]]) == False

Answer: assert Solution().isZeroArray(nums = [1,2,3,4,5], queries = [[0,0],[1,1],[2,2],[3,3],[4,4]]) == False

Answer: assert Solution().isZeroArray(nums = [3,3,3,3,3], queries = [[0,2],[1,3],[2,4]]) == False

Answer: assert Solution().isZeroArray(nums = [3,3,3], queries = [[0,2],[0,1],[1,2]]) == False

Answer: assert Solution().isZeroArray(nums = [2,2,2,2], queries = [[0,1],[2,3],[0,3]]) == True

Answer: assert Solution().isZeroArray(nums = [5,5,5,5], queries = [[0,3],[1,2],[2,3]]) == False

Answer: assert Solution().isZeroArray(nums = [3,3,3], queries = [[0,2],[0,2],[0,2]]) == True

Answer: assert Solution().isZeroArray(nums = [4,3,2,1], queries = [[1,3],[0,2]]) == False

Answer: assert Solution().isZeroArray(nums = [15,10,5,0,5,10,15], queries = [[0,6],[1,5],[2,4],[3,3],[0,3],[3,6],[1,4],[2,5]]) == False

Answer: assert Solution().isZeroArray(nums = [1,2,3,4,5,6,7,8,9,10], queries = [[0,9],[0,0],[9,9],[4,5],[3,6],[1,8],[2,7]]) == False

Answer: assert Solution().isZeroArray(nums = [10,9,8,7,6,5], queries = [[0,5],[1,4],[2,3],[3,2],[4,1],[5,0]]) == False

Answer: assert Solution().isZeroArray(nums = [1,0,1,0,1,0,1,0,1,0], queries = [[0,9],[1,8],[2,7],[3,6],[4,5],[5,4],[6,3],[7,2],[8,1],[9,0]]) == True

Answer: assert Solution().isZeroArray(nums = [0,1,2,3,4,5], queries = [[0,5],[0,0],[1,1],[2,2],[3,3],[4,4],[5,5]]) == False

Answer: assert Solution().isZeroArray(nums = [10,10,10,10,10,10], queries = [[0,5],[1,4],[2,3],[3,3],[0,2],[4,5]]) == False

Answer: assert Solution().isZeroArray(nums = [5,4,3,2,1], queries = [[0,4],[1,3],[2,2],[3,3],[4,4]]) == False

Answer: assert Solution().isZeroArray(nums = [10,10,10,10,10], queries = [[0,4],[0,3],[1,2],[2,1],[3,4]]) == False

Answer: assert Solution().isZeroArray(nums = [3,5,2,1,4], queries = [[0,1],[1,3],[2,4],[0,4]]) == False

Answer: assert Solution().isZeroArray(nums = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], queries = [[0,14],[1,13],[2,12],[3,11],[4,10],[5,9],[6,8],[7,7]]) == True

Answer: assert Solution().isZeroArray(nums = [100,50,25,10,5], queries = [[0,1],[1,2],[2,3],[3,4],[0,4]]) == False

Answer: assert Solution().isZeroArray(nums = [1,2,3,4,5,6], queries = [[0,5],[1,4],[2,3],[0,2],[3,5]]) == False

Answer: assert Solution().isZeroArray(nums = [8,7,6,5,4,3,2,1], queries = [[0,3],[1,4],[2,5],[3,6],[4,7],[0,4],[1,5],[2,6],[3,7]]) == False

Answer: assert Solution().isZeroArray(nums = [5,5,5,5,5,5,5,5,5,5], queries = [[0,2],[3,5],[6,8],[1,3],[4,6],[7,9],[0,4],[5,9]]) == False

Answer: assert Solution().isZeroArray(nums = [3,3,3,3,3,3], queries = [[0,5],[1,4],[2,3],[0,2],[3,5]]) == False

Answer: assert Solution().isZeroArray(nums = [5,10,15,20,25,30,35,40,45,50], queries = [[0,9],[1,8],[2,7],[3,6],[4,5],[0,4],[5,9],[1,7],[2,6],[3,5]]) == False

Answer: assert Solution().isZeroArray(nums = [3,3,3,3,3,3,3,3,3,3], queries = [[0,9],[1,8],[2,7],[3,6],[4,5],[0,4],[5,9],[1,7],[2,6],[3,5]]) == False

Answer: assert Solution().isZeroArray(nums = [2,4,6,8,10,12,14,16,18,20], queries = [[0,9],[0,4],[5,9],[0,2],[3,5],[6,8],[1,3],[4,6],[7,9],[0,9]]) == False

Answer: assert Solution().isZeroArray(nums = [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5], queries = [[0,14],[0,6],[7,13],[2,8],[3,10],[4,11],[5,12]]) == False

Answer: assert Solution().isZeroArray(nums = [1,2,3,4,5,6,7,8,9,10,11,12], queries = [[0,3],[4,7],[8,11],[0,11],[1,10],[2,9]]) == False

Answer: assert Solution().isZeroArray(nums = [1,2,3,4,5,6,7,8,9,10], queries = [[0,9],[1,8],[2,7],[3,6],[4,5],[5,4],[6,3],[7,2],[8,1],[9,0]]) == False

Answer: assert Solution().isZeroArray(nums = [1,0,2,0,3,0,4,0,5,0], queries = [[0,1],[2,3],[4,5],[6,7],[8,9],[0,9],[1,8],[2,7],[3,6],[4,5]]) == False

Answer: assert Solution().isZeroArray(nums = [3,3,3,3,3,3,3,3,3,3], queries = [[0,4],[5,9],[0,9],[1,8],[2,7],[3,6],[4,5],[0,2],[3,5],[6,8]]) == False

Answer: assert Solution().isZeroArray(nums = [1,2,3,4,5,6,7,8,9,10], queries = [[0,4],[5,9],[0,2],[7,9],[3,6]]) == False

Answer: assert Solution().isZeroArray(nums = [1,3,5,7,9,11,13,15,17,19], queries = [[0,9],[1,8],[2,7],[3,6],[4,5],[0,4],[5,9],[0,3],[2,5],[4,7]]) == False

Answer: assert Solution().isZeroArray(nums = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15], queries = [[0,14],[1,13],[2,12],[3,11],[4,10],[5,9],[6,8],[0,6],[7,13],[1,9],[2,8],[3,7],[4,5]]) == False

Answer: assert Solution().isZeroArray(nums = [3,3,3,3,3], queries = [[0,2],[1,3],[2,4],[0,4]]) == False

Answer: assert Solution().isZeroArray(nums = [3,2,1,0,1,2,3], queries = [[0,6],[1,5],[2,4],[3,3]]) == False

Answer: assert Solution().isZeroArray(nums = [3,3,3,3,3,3,3,3,3,3], queries = [[0,4],[5,9],[0,9],[0,2],[7,9]]) == False

Answer: assert Solution().isZeroArray(nums = [2,1,0,1,2,1,0,1,2,1], queries = [[0,9],[0,4],[5,9],[2,7],[3,6],[4,5]]) == True

Answer: assert Solution().isZeroArray(nums = [5,4,3,2,1], queries = [[0,4],[1,3],[2,2],[0,0],[3,4]]) == False

Answer: assert Solution().isZeroArray(nums = [0,1,2,3,4,5,6,7,8,9], queries = [[0,3],[3,6],[6,9],[0,9],[0,9]]) == False

Answer: assert Solution().isZeroArray(nums = [0,1,2,3,4,5,6,7,8,9,10], queries = [[1,10],[0,9],[2,8],[3,7],[4,6]]) == False

Answer: assert Solution().isZeroArray(nums = [10,20,30,40,50,60,70,80,90,100], queries = [[0,9],[0,4],[5,9],[2,7],[3,6],[4,5]]) == False

Answer: assert Solution().isZeroArray(nums = [1,2,3,4,5,6,7,8,9,10], queries = [[0,9],[1,8],[2,7],[3,6],[4,5]]) == False

Answer: assert Solution().isZeroArray(nums = [15,10,5,0,5,10,15], queries = [[0,6],[1,5],[2,4],[3,3],[0,2],[4,6]]) == False

Answer: assert Solution().isZeroArray(nums = [1,3,5,7,9], queries = [[0,4],[1,3],[2,2],[3,3],[0,1],[2,4]]) == False

Answer: assert Solution().isZeroArray(nums = [0,1,2,3,4,5,6,7,8,9,10], queries = [[0,10],[0,5],[5,10],[2,8],[4,6]]) == False

Answer: assert Solution().isZeroArray(nums = [1,2,3,4,5,6,7,8,9,10], queries = [[0,9],[0,0],[9,9],[1,8],[2,7],[3,6],[4,5]]) == False

Answer: assert Solution().isZeroArray(nums = [1,2,3,4,5,6,7,8,9,10], queries = [[0,9],[1,8],[2,7],[3,6],[4,5],[0,4],[5,9]]) == False

Answer: assert Solution().isZeroArray(nums = [5,4,3,2,1], queries = [[0,4],[1,3],[2,2],[0,1]]) == False

Answer: assert Solution().isZeroArray(nums = [1,1,1,1,1,1,1,1,1,1,1,1], queries = [[0,3],[4,7],[8,11],[0,11],[1,10],[2,9],[0,5],[6,11]]) == True

Answer: assert Solution().isZeroArray(nums = [5,6,7,8,9,10,11,12,13,14], queries = [[0,4],[5,9],[0,9],[1,8],[2,7],[3,6]]) == False

Answer: assert Solution().isZeroArray(nums = [7,0,5,0,3,0,2], queries = [[0,0],[2,2],[4,4],[6,6],[1,1],[3,3],[5,5]]) == False

Answer: assert Solution().isZeroArray(nums = [100,200,300,400,500], queries = [[0,4],[0,2],[1,3],[2,4],[3,4]]) == False

Answer: assert Solution().isZeroArray(nums = [1,1,1,1,1,1,1,1,1,1], queries = [[0,9],[0,9],[0,9],[0,9],[0,9]]) == True

Answer: assert Solution().isZeroArray(nums = [1,2,3,4,5,6,7,8,9,10], queries = [[0,5],[1,6],[2,7],[3,8],[4,9],[0,4],[5,9]]) == False

Answer: assert Solution().isZeroArray(nums = [0,1,2,3,4,5,6,7,8,9], queries = [[0,9],[0,9],[0,9],[0,9],[0,9],[0,9],[0,9],[0,9],[0,9],[0,9]]) == True

Answer: assert Solution().isZeroArray(nums = [5,4,3,2,1], queries = [[0,1],[1,2],[2,3],[3,4]]) == False

Answer: assert Solution().isZeroArray(nums = [10,9,8,7,6,5,4,3,2,1], queries = [[0,9],[1,8],[2,7],[3,6],[4,5],[0,4],[5,9]]) == False

Answer: assert Solution().isZeroArray(nums = [5,5,5,5,5,5,5,5,5,5], queries = [[0,4],[5,9],[0,4],[5,9],[0,4],[5,9]]) == False

Answer: assert Solution().isZeroArray(nums = [10,10,10,10,10,10,10,10,10,10,10,10], queries = [[0,3],[4,7],[8,11],[0,11],[1,10],[2,9],[0,5],[6,11]]) == False

Answer: assert Solution().isZeroArray(nums = [7,6,5,4,3,2,1], queries = [[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[6,6]]) == False

Answer: assert Solution().isZeroArray(nums = [5,4,3,2,1], queries = [[0,4],[1,3],[2,2],[3,4]]) == False

Answer: assert Solution().isZeroArray(nums = [1,1,1,1,1,1,1,1,1,1], queries = [[0,9],[0,4],[5,9],[2,6],[3,7]]) == True

Answer: assert Solution().isZeroArray(nums = [6,6,6,6,6,6,6], queries = [[0,3],[2,5],[1,4],[0,6],[3,3],[0,0],[6,6]]) == False

Answer: assert Solution().isZeroArray(nums = [1,0,1,0,1,0,1,0,1,0], queries = [[0,9],[1,8],[2,7],[3,6],[4,5]]) == True

Answer: assert Solution().isZeroArray(nums = [5,4,3,2,1], queries = [[0,4],[1,3],[2,2],[0,1],[3,4]]) == False

Answer: assert Solution().isZeroArray(nums = [2,2,2,2,2,2,2,2,2,2], queries = [[0,9],[1,8],[2,7],[3,6],[4,5],[0,4],[5,9]]) == True

Answer: assert Solution().isZeroArray(nums = [10,10,10,10,10,10,10,10,10,10], queries = [[0,4],[5,9],[0,9],[1,8],[2,7],[3,6],[4,5],[0,2],[3,5],[6,8],[0,0],[9,9],[1,1],[2,2],[3,3],[4,4],[5,5],[6,6],[7,7],[8,8]]) == False

Answer: assert Solution().isZeroArray(nums = [5,5,5,5,5], queries = [[0,4],[0,2],[3,4],[1,3]]) == False

Answer: assert Solution().isZeroArray(nums = [5,5,5,5,5,5,5,5,5,5], queries = [[0,4],[5,9],[0,2],[7,9],[3,6],[0,9],[0,9]]) == False

Answer: assert Solution().isZeroArray(nums = [1,2,3,4,5,6,7,8,9,10], queries = [[0,4],[5,9],[0,2],[3,5],[6,8],[1,3],[4,7],[2,6],[0,9]]) == False

Answer: assert Solution().isZeroArray(nums = [1,3,2,3,1], queries = [[0,2],[2,4],[0,1],[3,4],[1,3]]) == True

Answer: assert Solution().isZeroArray(nums = [1,0,0,1,0,1,0,1,0,1], queries = [[0,9],[1,8],[2,7],[3,6],[4,5],[0,4],[5,9],[2,6],[1,3]]) == True

Answer: assert Solution().isZeroArray(nums = [100,50,25,10,5,2,1], queries = [[0,6],[1,5],[2,4],[3,3],[0,2],[4,6],[5,5],[6,6],[0,1],[2,3]]) == False

Answer: assert Solution().isZeroArray(nums = [0,1,2,3,4,5,6,7,8,9,10], queries = [[0,10],[1,9],[2,8],[3,7],[4,6],[0,5],[6,10],[1,8],[2,7],[3,6],[4,5]]) == False

Answer: assert Solution().isZeroArray(nums = [1,1,1,1,1,1,1,1,1,1], queries = [[0,4],[5,9],[0,9],[1,8],[2,7]]) == True

Answer: assert Solution().isZeroArray(nums = [1,2,1,2,1,2,1,2,1,2], queries = [[0,9],[1,8],[2,7],[3,6],[4,5],[0,4],[5,9],[1,7],[2,6],[3,5]]) == True

Answer: assert Solution().isZeroArray(nums = [10,0,10,0,10,0,10,0,10,0], queries = [[0,4],[4,8],[0,9],[2,6],[1,7]]) == False

Answer: assert Solution().isZeroArray(nums = [10,20,30,40,50,60,70,80,90,100], queries = [[0,9],[1,8],[2,7],[3,6],[4,5],[0,4],[5,9],[1,7],[2,6],[3,5]]) == False

Answer: assert Solution().isZeroArray(nums = [10,20,30,40,50], queries = [[0,4],[0,2],[2,4],[1,3],[0,1],[3,4]]) == False

Answer: assert Solution().isZeroArray(nums = [1,1,1,1,1,1], queries = [[0,2],[2,4],[0,5],[1,3],[4,5]]) == True

Answer: assert Solution().isZeroArray(nums = [3,0,2,0,1,4], queries = [[0,1],[2,3],[1,4],[0,5],[2,5]]) == False

Answer: assert Solution().isZeroArray(nums = [1,1,2,2,3,3], queries = [[0,1],[2,3],[4,5],[0,2],[1,4],[2,5]]) == False

Answer: assert Solution().isZeroArray(nums = [1,0,1,0,1,0,1,0,1,0], queries = [[0,1],[2,3],[4,5],[6,7],[8,9],[0,9],[1,8],[2,7],[3,6],[4,5]]) == True

Answer: assert Solution().isZeroArray(nums = [7,6,5,4,3,2,1], queries = [[0,6],[1,5],[2,4],[3,3],[0,2],[4,6]]) == False

Answer: assert Solution().isZeroArray(nums = [3,3,3,3,3,3,3,3,3,3], queries = [[0,9],[1,8],[2,7],[3,6],[4,5],[0,4],[5,9]]) == False

Answer: assert Solution().isZeroArray(nums = [1,1,1,1,1,1,1,1,1,1], queries = [[0,9],[1,8],[2,7],[3,6],[4,5],[0,4],[5,9]]) == True

Answer: assert Solution().isZeroArray(nums = [1,1,1,1,1,1], queries = [[0,2],[3,5],[1,4],[0,5]]) == True

Answer: assert Solution().isZeroArray(nums = [1,2,2,3,3,3,4,4,4,4], queries = [[0,1],[2,3],[4,5],[6,7],[8,9],[0,9]]) == False

Answer: assert Solution().isZeroArray(nums = [0,1,2,3,4,5,6,7,8,9], queries = [[0,9],[1,8],[2,7],[3,6],[4,5],[0,4],[5,9],[2,6],[1,3]]) == False

Answer: assert Solution().isZeroArray(nums = [1,0,2,0,3,0,4,0,5,0], queries = [[0,9],[1,8],[2,7],[3,6],[4,5]]) == False

Answer: assert Solution().isZeroArray(nums = [7,7,7,7,7,7,7], queries = [[0,1],[1,2],[2,3],[3,4],[4,5],[5,6]]) == False

Answer: assert Solution().isZeroArray(nums = [1,2,3,4,5,6,7,8,9,10], queries = [[0,9],[1,8],[2,7],[3,6],[4,5],[0,4],[5,9],[2,6]]) == False

import random
import functools
import collections
import string
import math
import datetime

from typing import *
from functools import *
from collections import *
from itertools import *
from heapq import *
from bisect import *
from string import *
from operator import *
from math import *

inf = float('inf')

class ListNode:
    def __init__(self, val=0, next=None):
        self.val = val
        self.next = next

def list_node(values: list):
    if not values:
        return None
    head = ListNode(values[0])
    p = head
    for val in values[1:]:
        node = ListNode(val)
        p.next = node
        p = node
    return head

def is_same_list(p1, p2):
    if p1 is None and p2 is None:
        return True
    if not p1 or not p2:
        return False
    return p1.val == p2.val and is_same_list(p1.next, p2.next)

class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def tree_node(values: list):
    if not values:
        return None
    root = TreeNode(values[0])
    i = 1
    queue = deque()
    queue.append(root)
    while queue:
        node = queue.popleft()
        if i < len(values) and values[i] is not None:
            node.left = TreeNode(values[i])
            queue.append(node.left)
        i += 1
        if i < len(values) and values[i] is not None:
            node.right = TreeNode(values[i])
            queue.append(node.right)
        i += 1
    return root

def is_same_tree(p, q):
    if not p and not q:
        return True
    elif not p or not q:
        return False
    elif p.val != q.val:
        return False
    else:
        return is_same_tree(p.left, q.left) and is_same_tree(p.right, q.right)

class Solution:
    def isZeroArray(self, nums: List[int], queries: List[List[int]]) -> bool:
        d = [0] * (len(nums) + 1)
        for l, r in queries:
            d[l] += 1
            d[r + 1] -= 1
        s = 0
        for x, y in zip(nums, d):
            s += y
            if x > s:
                return False
        return True


You are an expert Python programmer. Write correct, efficient Python 3 code that solves the problem and passes all tests. Output the code in the following format: ```python
<code>
```

PROBLEM:
You are given an integer array nums of length n and a 2D array queries where queries[i] = [li, ri, vali].
Each queries[i] represents the following action on nums:

Decrement the value at each index in the range [li, ri] in nums by at most vali.
The amount by which each value is decremented can be chosen independently for each index.

A Zero Array is an array with all its elements equal to 0.
Return the minimum possible non-negative value of k, such that after processing the first k queries in sequence, nums becomes a Zero Array. If no such k exists, return -1.

Example 1:

Input: nums = [2,0,2], queries = [[0,2,1],[0,2,1],[1,1,3]]
Output: 2
Explanation:

For i = 0 (l = 0, r = 2, val = 1):

Decrement values at indices [0, 1, 2] by [1, 0, 1] respectively.
The array will become [1, 0, 1].

For i = 1 (l = 0, r = 2, val = 1):

Decrement values at indices [0, 1, 2] by [1, 0, 1] respectively.
The array will become [0, 0, 0], which is a Zero Array. Therefore, the minimum value of k is 2.

Example 2:

Input: nums = [4,3,2,1], queries = [[1,3,2],[0,2,1]]
Output: -1
Explanation:

For i = 0 (l = 1, r = 3, val = 2):

Decrement values at indices [1, 2, 3] by [2, 2, 1] respectively.
The array will become [4, 1, 0, 0].

For i = 1 (l = 0, r = 2, val = 1):

Decrement values at indices [0, 1, 2] by [1, 1, 0] respectively.
The array will become [3, 0, 0, 0], which is not a Zero Array.

Constraints:

1 <= nums.length <= 105
0 <= nums[i] <= 5 * 105
1 <= queries.length <= 105
queries[i].length == 3
0 <= li <= ri < nums.length
1 <= vali <= 5

Your solution to the problem should be a method of the class Solution called minZeroArray and should pass all tests. Use the following starter code:
```python
class Solution:
    def minZeroArray(self, nums: List[int], queries: List[List[int]]) -> int:
        # Add your code here
```

SOLUTION:

Question:
PROBLEM:
You are given an integer array nums of length n and a 2D array queries where queries[i] = [li, ri, vali].
Each queries[i] represents the following action on nums:

Decrement the value at each index in the range [li, ri] in nums by at most vali.
The amount by which each value is decremented can be chosen independently for each index.

A Zero Array is an array with all its elements equal to 0.
Return the minimum possible non-negative value of k, such that after processing the first k queries in sequence, nums becomes a Zero Array. If no such k exists, return -1.

Example 1:

Input: nums = [2,0,2], queries = [[0,2,1],[0,2,1],[1,1,3]]
Output: 2
Explanation:

For i = 0 (l = 0, r = 2, val = 1):

Decrement values at indices [0, 1, 2] by [1, 0, 1] respectively.
The array will become [1, 0, 1].

For i = 1 (l = 0, r = 2, val = 1):

Decrement values at indices [0, 1, 2] by [1, 0, 1] respectively.
The array will become [0, 0, 0], which is a Zero Array. Therefore, the minimum value of k is 2.

Example 2:

Input: nums = [4,3,2,1], queries = [[1,3,2],[0,2,1]]
Output: -1
Explanation:

For i = 0 (l = 1, r = 3, val = 2):

Decrement values at indices [1, 2, 3] by [2, 2, 1] respectively.
The array will become [4, 1, 0, 0].

For i = 1 (l = 0, r = 2, val = 1):

Decrement values at indices [0, 1, 2] by [1, 1, 0] respectively.
The array will become [3, 0, 0, 0], which is not a Zero Array.

Constraints:

1 <= nums.length <= 105
0 <= nums[i] <= 5 * 105
1 <= queries.length <= 105
queries[i].length == 3
0 <= li <= ri < nums.length
1 <= vali <= 5

Your solution to the problem should be a method of the class Solution called minZeroArray and should pass all tests. Use the following starter code:
```python
class Solution:
    def minZeroArray(self, nums: List[int], queries: List[List[int]]) -> int:
        # Add your code here
```

SOLUTION:

Answer: assert Solution().minZeroArray(nums = [2,0,2], queries = [[0,2,1],[0,2,1],[1,1,3]]) == 2

Answer: assert Solution().minZeroArray(nums = [4,3,2,1], queries = [[1,3,2],[0,2,1]]) == -1

Answer: assert Solution().minZeroArray(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], queries = [[0, 0, 3], [1, 1, 3], [2, 2, 3], [3, 3, 3], [4, 4, 3], [5, 5, 3], [6, 6, 3], [7, 7, 3], [8, 8, 3], [9, 9, 3]]) == 10

Answer: assert Solution().minZeroArray(nums = [1,1,1,1,1,1,1,1,1,1], queries = [[0,9,1],[0,4,1],[5,9,1],[0,9,1],[0,9,1]]) == 1

Answer: assert Solution().minZeroArray(nums = [10,10,10,10,10,10,10,10,10,10], queries = [[0,9,5],[0,9,5],[0,9,5],[0,9,5],[0,9,5]]) == 2

Answer: assert Solution().minZeroArray(nums = [100,200,300,400,500,600,700,800,900,1000], queries = [[0,4,100],[5,9,200],[0,9,100],[0,9,200],[0,9,300]]) == -1

Answer: assert Solution().minZeroArray(nums = [1,1,1,1,1,1,1,1,1,1], queries = [[0,9,1],[1,8,1],[2,7,1],[3,6,1],[4,5,1]]) == 1

Answer: assert Solution().minZeroArray(nums = [5,10,15,20,25,30,35,40,45,50], queries = [[0,4,10],[5,9,10],[0,9,5],[0,9,3],[0,9,1]]) == -1

Answer: assert Solution().minZeroArray(nums = [5,5,5,5,5,5,5,5,5,5], queries = [[0,9,5],[0,9,5],[0,9,5],[0,9,5],[0,9,5]]) == 1

Answer: assert Solution().minZeroArray(nums = [100,200,300,400,500], queries = [[0,0,100],[1,1,200],[2,2,300],[3,3,400],[4,4,500]]) == 5

Answer: assert Solution().minZeroArray(nums = [5,5,5,5,5], queries = [[0,4,5],[1,3,3],[2,2,1]]) == 1

Answer: assert Solution().minZeroArray(nums = [500000,500000,500000,500000,500000], queries = [[0,4,500000],[0,4,500000],[0,4,500000],[0,4,500000],[0,4,500000]]) == 1

Answer: assert Solution().minZeroArray(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], queries = [[0, 9, 1], [1, 8, 2], [2, 7, 3], [3, 6, 4], [4, 5, 5], [0, 9, 1], [1, 8, 2], [2, 7, 3], [3, 6, 4], [4, 5, 5]]) == -1

Answer: assert Solution().minZeroArray(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30], queries = [[0, 4, 3], [5, 9, 3], [2, 7, 6], [1, 8, 3], [0, 9, 1]]) == -1

Answer: assert Solution().minZeroArray(nums = [5,4,3,2,1], queries = [[0,0,5],[1,1,4],[2,2,3],[3,3,2],[4,4,1]]) == 5

Answer: assert Solution().minZeroArray(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10], queries = [[0, 4, 5], [5, 9, 5], [0, 9, 5], [0, 9, 5], [0, 9, 5], [0, 9, 5], [0, 9, 5], [0, 9, 5], [0, 9, 5], [0, 9, 5]]) == 3

Answer: assert Solution().minZeroArray(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19], queries = [[0, 9, 1], [1, 8, 2], [2, 7, 3], [3, 6, 4], [4, 5, 5]]) == -1

Answer: assert Solution().minZeroArray(nums = [50000,50000,50000,50000,50000], queries = [[0,4,5],[0,4,5],[0,4,5],[0,4,5],[0,4,5],[0,4,5],[0,4,5],[0,4,5],[0,4,5],[0,4,5]]) == -1

Answer: assert Solution().minZeroArray(nums = [5,0,5,0,5,0,5,0,5,0], queries = [[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1]]) == 5

Answer: assert Solution().minZeroArray(nums = [10,9,8,7,6,5,4,3,2,1], queries = [[0,9,1],[0,9,2],[0,9,3],[0,9,4],[0,9,5]]) == 4

Answer: assert Solution().minZeroArray(nums = [1,2,3,4,5,6,7,8,9,10], queries = [[0,0,1],[1,1,1],[2,2,1],[3,3,1],[4,4,1],[5,5,1],[6,6,1],[7,7,1],[8,8,1],[9,9,1]]) == -1

Answer: assert Solution().minZeroArray(nums = [3,3,3,3,3], queries = [[0,4,1],[0,4,1],[0,4,1],[0,4,1],[0,4,1]]) == 3

Answer: assert Solution().minZeroArray(nums = [5,5,5,5,5,5,5,5,5,5], queries = [[0,4,2],[5,9,2],[0,4,2],[5,9,2],[0,4,2],[5,9,2]]) == 6

Answer: assert Solution().minZeroArray(nums = [10,10,10,10,10,10,10,10,10,10], queries = [[0,4,2],[5,9,2],[0,9,1],[0,9,1],[0,9,1]]) == -1

Answer: assert Solution().minZeroArray(nums = [5, 5, 5, 5, 5], queries = [[0, 4, 5], [0, 4, 5], [0, 4, 5], [0, 4, 5], [0, 4, 5]]) == 1

Answer: assert Solution().minZeroArray(nums = [3,6,9,12,15,18,21,24,27,30], queries = [[0,2,3],[1,3,6],[2,4,9],[3,5,12],[4,6,15],[5,7,18],[6,8,21],[7,9,24]]) == -1

Answer: assert Solution().minZeroArray(nums = [100,100,100,100,100], queries = [[0,4,20],[0,4,20],[0,4,20],[0,4,20],[0,4,20]]) == 5

Answer: assert Solution().minZeroArray(nums = [1,1,1,1,1,1,1,1,1,1], queries = [[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1]]) == 1

Answer: assert Solution().minZeroArray(nums = [10,20,30,40,50], queries = [[0,0,10],[1,1,10],[2,2,10],[3,3,10],[4,4,10]]) == -1

Answer: assert Solution().minZeroArray(nums = [3,3,3,3,3], queries = [[0,2,2],[1,3,2],[2,4,2],[0,4,2]]) == 4

Answer: assert Solution().minZeroArray(nums = [1,1,1,1,1,1,1,1,1,1], queries = [[0,0,1],[1,1,1],[2,2,1],[3,3,1],[4,4,1],[5,5,1],[6,6,1],[7,7,1],[8,8,1],[9,9,1]]) == 10

Answer: assert Solution().minZeroArray(nums = [10,20,30,40,50], queries = [[0,4,10],[0,4,10],[0,4,10],[0,4,10],[0,4,10]]) == 5

Answer: assert Solution().minZeroArray(nums = [5,5,5,5,5], queries = [[0,4,1],[0,4,1],[0,4,1],[0,4,1],[0,4,1]]) == 5

Answer: assert Solution().minZeroArray(nums = [100,200,300,400,500], queries = [[0,4,100],[0,4,100],[0,4,100],[0,4,100],[0,4,100],[0,4,100]]) == 5

Answer: assert Solution().minZeroArray(nums = [1,1,1,1,1,1,1,1,1,1], queries = [[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1]]) == 1

Answer: assert Solution().minZeroArray(nums = [10,9,8,7,6,5,4,3,2,1], queries = [[0,9,2],[1,8,2],[2,7,2],[3,6,2],[4,5,2]]) == -1

Answer: assert Solution().minZeroArray(nums = [10,20,30,40,50], queries = [[0,2,5],[1,4,3],[2,3,2],[3,4,1]]) == -1

Answer: assert Solution().minZeroArray(nums = [3,3,3,3,3,3,3,3,3,3], queries = [[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1]]) == 3

Answer: assert Solution().minZeroArray(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], queries = [[0, 9, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1]]) == 10

Answer: assert Solution().minZeroArray(nums = [5,5,5,5,5,5,5,5,5,5], queries = [[0,4,1],[5,9,1],[0,4,1],[5,9,1],[0,4,1],[5,9,1]]) == -1

Answer: assert Solution().minZeroArray(nums = [1,2,3,4,5,6,7,8,9,10], queries = [[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1]]) == 10

Answer: assert Solution().minZeroArray(nums = [1,2,3,4,5,4,3,2,1], queries = [[0,8,1],[0,8,1],[0,8,1],[0,8,1],[0,8,1]]) == 5

Answer: assert Solution().minZeroArray(nums = [1,2,3,4,5,6,7,8,9,10], queries = [[0,9,3],[0,9,3],[0,9,3],[0,9,3],[0,9,3]]) == 4

Answer: assert Solution().minZeroArray(nums = [10,9,8,7,6,5,4,3,2,1], queries = [[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1]]) == -1

Answer: assert Solution().minZeroArray(nums = [1,1,1,1,1,1,1,1,1,1], queries = [[0,4,1],[5,9,1],[0,2,1],[3,5,1],[6,8,1]]) == 2

Answer: assert Solution().minZeroArray(nums = [5,4,3,2,1,0,1,2,3,4,5], queries = [[0,10,1],[1,9,2],[2,8,3],[3,7,4],[4,6,5]]) == -1

Answer: assert Solution().minZeroArray(nums = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], queries = [[0,19,1],[0,19,1],[0,19,1],[0,19,1],[0,19,1]]) == 1

Answer: assert Solution().minZeroArray(nums = [5,10,15,20,25,30,35,40,45,50], queries = [[0,9,5],[0,9,5],[0,9,5],[0,9,5],[0,9,5],[0,9,5]]) == -1

Answer: assert Solution().minZeroArray(nums = [15, 10, 5, 0], queries = [[0, 0, 15], [1, 1, 10], [2, 2, 5], [3, 3, 1]]) == 3

Answer: assert Solution().minZeroArray(nums = [10,20,30,40,50,60,70,80,90,100], queries = [[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10]]) == 10

Answer: assert Solution().minZeroArray(nums = [100000,100000,100000,100000,100000,100000,100000,100000,100000,100000], queries = [[0,9,5],[0,9,5],[0,9,5],[0,9,5],[0,9,5],[0,9,5],[0,9,5],[0,9,5],[0,9,5],[0,9,5]]) == -1

Answer: assert Solution().minZeroArray(nums = [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5], queries = [[0,14,5],[1,13,5],[2,12,5],[3,11,5],[4,10,5]]) == 1

Answer: assert Solution().minZeroArray(nums = [10, 20, 30, 40, 50], queries = [[0, 4, 5], [1, 3, 10], [2, 3, 5], [0, 1, 20]]) == -1

Answer: assert Solution().minZeroArray(nums = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15], queries = [[0,14,1],[1,13,2],[2,12,3],[3,11,4],[4,10,5]]) == -1

Answer: assert Solution().minZeroArray(nums = [10,20,30,40,50], queries = [[0,0,10],[1,1,20],[2,2,30],[3,3,40],[4,4,50]]) == 5

Answer: assert Solution().minZeroArray(nums = [5,0,5,0,5,0,5,0,5,0], queries = [[0,9,5],[1,8,5],[2,7,5],[3,6,5],[4,5,5]]) == 1

Answer: assert Solution().minZeroArray(nums = [0,0,0,0,0,0,0,0,0,0], queries = [[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1]]) == 0

Answer: assert Solution().minZeroArray(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5], queries = [[0, 4, 2], [5, 9, 2], [2, 7, 3], [1, 8, 1]]) == -1

Answer: assert Solution().minZeroArray(nums = [10,20,30,40,50,60,70,80,90,100], queries = [[0,4,10],[5,9,20],[0,9,30],[0,9,40],[0,9,50]]) == 5

Answer: assert Solution().minZeroArray(nums = [1,2,3,4,5,6,7,8,9,10], queries = [[0,9,1],[1,8,2],[2,7,3],[3,6,4],[4,5,5]]) == -1

Answer: assert Solution().minZeroArray(nums = [10,10,10,10,10], queries = [[0,2,2],[3,4,3],[0,1,2],[2,3,1]]) == -1

Answer: assert Solution().minZeroArray(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], queries = [[0, 4, 10], [5, 9, 10], [0, 9, 5], [0, 9, 5], [0, 9, 5]]) == -1

Answer: assert Solution().minZeroArray(nums = [5,5,5,5,5,5,5,5,5,5], queries = [[0,9,5],[0,9,5],[0,9,5],[0,9,5],[0,9,5],[0,9,5],[0,9,5],[0,9,5],[0,9,5],[0,9,5]]) == 1

Answer: assert Solution().minZeroArray(nums = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], queries = [[0,19,1],[1,18,2],[2,17,3],[3,16,4],[4,15,5]]) == 1

Answer: assert Solution().minZeroArray(nums = [3,3,3,3,3,3,3,3,3,3], queries = [[0,9,3],[0,9,3],[0,9,3],[0,9,3],[0,9,3],[0,9,3]]) == 1

Answer: assert Solution().minZeroArray(nums = [5,4,3,2,1], queries = [[0,4,1],[1,3,2],[2,2,3],[0,0,5]]) == -1

Answer: assert Solution().minZeroArray(nums = [1, 2, 3, 4, 5], queries = [[0, 2, 2], [3, 4, 3], [1, 3, 1], [0, 1, 1], [2, 4, 2]]) == 5

Answer: assert Solution().minZeroArray(nums = [10,9,8,7,6,5,4,3,2,1], queries = [[0,9,1],[1,8,2],[2,7,3],[3,6,4],[4,5,5]]) == -1

Answer: assert Solution().minZeroArray(nums = [1,2,3,4,5], queries = [[0,2,1],[3,4,1],[0,1,2],[2,3,2],[1,2,3]]) == -1

Answer: assert Solution().minZeroArray(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], queries = [[0, 9, 1], [1, 8, 2], [2, 7, 3], [3, 6, 4]]) == -1

Answer: assert Solution().minZeroArray(nums = [500,400,300,200,100], queries = [[0,1,100],[1,2,200],[2,3,300],[3,4,400],[4,4,500]]) == -1

Answer: assert Solution().minZeroArray(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], queries = [[0, 0, 1], [1, 1, 1], [2, 2, 1], [3, 3, 1], [4, 4, 1], [5, 5, 1], [6, 6, 1], [7, 7, 1], [8, 8, 1], [9, 9, 1]]) == 10

Answer: assert Solution().minZeroArray(nums = [5, 4, 3, 2, 1], queries = [[0, 0, 5], [1, 1, 4], [2, 2, 3], [3, 3, 2], [4, 4, 1]]) == 5

Answer: assert Solution().minZeroArray(nums = [30,20,10,0,10,20,30], queries = [[0,6,5],[0,6,5],[0,6,5],[0,6,5],[0,6,5]]) == -1

Answer: assert Solution().minZeroArray(nums = [2,4,6,8,10,12,14,16,18,20], queries = [[0,9,2],[0,9,4],[0,9,6],[0,9,8],[0,9,10]]) == 4

Answer: assert Solution().minZeroArray(nums = [100,200,300,400,500], queries = [[0,0,500],[1,1,200],[2,2,300],[3,3,400],[4,4,100]]) == -1

Answer: assert Solution().minZeroArray(nums = [100, 200, 300, 400, 500], queries = [[0, 4, 100], [1, 3, 200], [2, 3, 150], [0, 1, 300]]) == -1

Answer: assert Solution().minZeroArray(nums = [3,3,3,3,3,3,3,3,3,3], queries = [[0,4,2],[5,9,2],[0,3,1],[4,7,1],[7,9,1]]) == 5

Answer: assert Solution().minZeroArray(nums = [1,2,3,4,5], queries = [[0,0,1],[1,1,2],[2,2,3],[3,3,4],[4,4,5]]) == 5

Answer: assert Solution().minZeroArray(nums = [5,5,5,5,5,5,5,5,5,5], queries = [[0,4,5],[5,9,5],[0,9,5]]) == 2

Answer: assert Solution().minZeroArray(nums = [1,2,3,4,5,6,7,8,9,10], queries = [[0,4,1],[5,9,1],[0,4,2],[5,9,2],[0,4,3],[5,9,3],[0,4,4],[5,9,4],[0,4,5],[5,9,5]]) == 8

Answer: assert Solution().minZeroArray(nums = [3,3,3,3,3,3,3,3,3,3], queries = [[0,4,1],[5,9,1],[0,4,1],[5,9,1],[0,4,1]]) == -1

Answer: assert Solution().minZeroArray(nums = [0,0,0,0,0], queries = [[0,4,1],[0,4,1],[0,4,1]]) == 0

Answer: assert Solution().minZeroArray(nums = [5,4,3,2,1], queries = [[0,4,1],[0,4,1],[0,4,1],[0,4,1],[0,4,1]]) == 5

Answer: assert Solution().minZeroArray(nums = [1,2,3,4,5,6,7,8,9,10], queries = [[0,9,5],[0,9,5],[0,9,5],[0,9,5],[0,9,5]]) == 2

Answer: assert Solution().minZeroArray(nums = [0, 0, 0, 0, 0], queries = [[0, 4, 10], [1, 3, 5], [2, 2, 3]]) == 0

Answer: assert Solution().minZeroArray(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10], queries = [[0, 4, 3], [5, 9, 3], [2, 7, 4], [0, 9, 2]]) == -1

import random
import functools
import collections
import string
import math
import datetime

from typing import *
from functools import *
from collections import *
from itertools import *
from heapq import *
from bisect import *
from string import *
from operator import *
from math import *

inf = float('inf')

class ListNode:
    def __init__(self, val=0, next=None):
        self.val = val
        self.next = next

def list_node(values: list):
    if not values:
        return None
    head = ListNode(values[0])
    p = head
    for val in values[1:]:
        node = ListNode(val)
        p.next = node
        p = node
    return head

def is_same_list(p1, p2):
    if p1 is None and p2 is None:
        return True
    if not p1 or not p2:
        return False
    return p1.val == p2.val and is_same_list(p1.next, p2.next)

class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def tree_node(values: list):
    if not values:
        return None
    root = TreeNode(values[0])
    i = 1
    queue = deque()
    queue.append(root)
    while queue:
        node = queue.popleft()
        if i < len(values) and values[i] is not None:
            node.left = TreeNode(values[i])
            queue.append(node.left)
        i += 1
        if i < len(values) and values[i] is not None:
            node.right = TreeNode(values[i])
            queue.append(node.right)
        i += 1
    return root

def is_same_tree(p, q):
    if not p and not q:
        return True
    elif not p or not q:
        return False
    elif p.val != q.val:
        return False
    else:
        return is_same_tree(p.left, q.left) and is_same_tree(p.right, q.right)

class Solution:
    def minZeroArray(self, nums: List[int], queries: List[List[int]]) -> int:
        def check(k: int) -> bool:
            d = [0] * (len(nums) + 1)
            for l, r, val in queries[:k]:
                d[l] += val
                d[r + 1] -= val
            s = 0
            for x, y in zip(nums, d):
                s += y
                if x > s:
                    return False
            return True

        m = len(queries)
        l = bisect_left(range(m + 1), True, key=check)
        return -1 if l > m else l