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 an integer array queries.
Let gcdPairs denote an array obtained by calculating the GCD of all possible pairs (nums[i], nums[j]), where 0 <= i < j < n, and then sorting these values in ascending order.
For each query queries[i], you need to find the element at index queries[i] in gcdPairs.
Return an integer array answer, where answer[i] is the value at gcdPairs[queries[i]] for each query.
The term gcd(a, b) denotes the greatest common divisor of a and b.

Example 1:

Input: nums = [2,3,4], queries = [0,2,2]
Output: [1,2,2]
Explanation:
gcdPairs = [gcd(nums[0], nums[1]), gcd(nums[0], nums[2]), gcd(nums[1], nums[2])] = [1, 2, 1].
After sorting in ascending order, gcdPairs = [1, 1, 2].
So, the answer is [gcdPairs[queries[0]], gcdPairs[queries[1]], gcdPairs[queries[2]]] = [1, 2, 2].

Example 2:

Input: nums = [4,4,2,1], queries = [5,3,1,0]
Output: [4,2,1,1]
Explanation:
gcdPairs sorted in ascending order is [1, 1, 1, 2, 2, 4].

Example 3:

Input: nums = [2,2], queries = [0,0]
Output: [2,2]
Explanation:
gcdPairs = [2].

Constraints:

2 <= n == nums.length <= 105
1 <= nums[i] <= 5 * 104
1 <= queries.length <= 105
0 <= queries[i] < n * (n - 1) / 2

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

SOLUTION:

Question:
PROBLEM:
You are given an integer array nums of length n and an integer array queries.
Let gcdPairs denote an array obtained by calculating the GCD of all possible pairs (nums[i], nums[j]), where 0 <= i < j < n, and then sorting these values in ascending order.
For each query queries[i], you need to find the element at index queries[i] in gcdPairs.
Return an integer array answer, where answer[i] is the value at gcdPairs[queries[i]] for each query.
The term gcd(a, b) denotes the greatest common divisor of a and b.

Example 1:

Input: nums = [2,3,4], queries = [0,2,2]
Output: [1,2,2]
Explanation:
gcdPairs = [gcd(nums[0], nums[1]), gcd(nums[0], nums[2]), gcd(nums[1], nums[2])] = [1, 2, 1].
After sorting in ascending order, gcdPairs = [1, 1, 2].
So, the answer is [gcdPairs[queries[0]], gcdPairs[queries[1]], gcdPairs[queries[2]]] = [1, 2, 2].

Example 2:

Input: nums = [4,4,2,1], queries = [5,3,1,0]
Output: [4,2,1,1]
Explanation:
gcdPairs sorted in ascending order is [1, 1, 1, 2, 2, 4].

Example 3:

Input: nums = [2,2], queries = [0,0]
Output: [2,2]
Explanation:
gcdPairs = [2].

Constraints:

2 <= n == nums.length <= 105
1 <= nums[i] <= 5 * 104
1 <= queries.length <= 105
0 <= queries[i] < n * (n - 1) / 2

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

SOLUTION:

assert Solution().gcdValues(nums = [5,10,15], queries = [0,1,2]) == [5, 5, 5]

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

assert Solution().gcdValues(nums = [2,2], queries = [0,0]) == [2, 2]

Answer: assert Solution().gcdValues(nums = [5,10,15,20], queries = [0,1,2,3,4,5,6,8]) == [5, 5, 5, 5, 5, 10, 21, 21]

Answer: assert Solution().gcdValues(nums = [7,14,28,35], queries = [0,3,5,10]) == [7, 7, 14, 36]

Answer: assert Solution().gcdValues(nums = [7,14,21,28,35], queries = [0,1,2,3,4,5,6,7,8,9,10]) == [7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 36]

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

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

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

Answer: assert Solution().gcdValues(nums = [3,6,9,12], queries = [0,1,2,3,4,5]) == [3, 3, 3, 3, 3, 6]

Answer: assert Solution().gcdValues(nums = [5,10,15,20,25], queries = [0,6,9,10]) == [5, 5, 10, 26]

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

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

Answer: assert Solution().gcdValues(nums = [2,2], queries = [0,0]) == [2, 2]

Answer: assert Solution().gcdValues(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], queries = [0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

Answer: assert Solution().gcdValues(nums = [10000, 10001, 10002, 10003, 10004, 10005], queries = [0, 14, 15, 16, 17, 18, 19, 20]) == [1, 5, 10006, 10006, 10006, 10006, 10006, 10006]

Answer: assert Solution().gcdValues(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384], queries = [0, 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, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 32, 32, 32, 32, 32, 32, 32, 32, 32, 64, 64, 64, 64, 64, 64, 64, 64, 128, 128, 128, 128, 128, 128, 128, 256, 256, 256, 256, 256, 256, 512, 512, 512, 512, 512, 1024, 1024, 1024, 1024, 2048, 2048, 2048, 4096, 4096, 8192, 16385, 16385, 16385, 16385, 16385, 16385, 16385, 16385, 16385, 16385, 16385, 16385, 16385, 16385, 16385, 16385, 16385, 16385, 16385, 16385, 16385, 16385, 16385]

Answer: assert Solution().gcdValues(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], queries = [0, 20, 40, 50, 60]) == [1, 1, 1, 1, 1]

Answer: assert Solution().gcdValues(nums = [12, 15, 20, 25, 30, 35], queries = [0, 10, 15, 20, 25]) == [1, 5, 36, 36, 36]

Answer: assert Solution().gcdValues(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], queries = [0, 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, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45]) == [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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 5, 11]

Answer: assert Solution().gcdValues(nums = [17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238, 255], queries = [0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150]) == [17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 34, 34, 34, 51, 51, 85, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256]

Answer: assert Solution().gcdValues(nums = [12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99], queries = [0,49,98,147,196,245,292]) == [3, 3, 3, 3, 3, 3, 6]

Answer: assert Solution().gcdValues(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45], queries = [0, 10, 20, 30, 40, 50, 60, 70, 80, 90]) == [3, 3, 3, 3, 3, 3, 3, 3, 6, 9]

Answer: assert Solution().gcdValues(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30], queries = [4, 9, 14, 19, 24, 29]) == [3, 3, 3, 3, 3, 3]

Answer: assert Solution().gcdValues(nums = [17, 34, 51, 68, 85, 102, 119, 136, 153, 170], queries = [0, 44, 45, 46, 47, 48]) == [17, 85, 171, 171, 171, 171]

Answer: assert Solution().gcdValues(nums = [100, 200, 300, 400, 500], queries = [0, 4, 8, 10, 14]) == [100, 100, 100, 501, 501]

Answer: assert Solution().gcdValues(nums = [10000, 15000, 20000, 25000, 30000], queries = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == [5000, 5000, 5000, 5000, 5000, 5000, 10000, 10000, 10000, 15000]

Answer: assert Solution().gcdValues(nums = [2000, 1500, 1000, 500, 250, 125, 62, 31], queries = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]) == [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 31, 125, 125, 125, 125, 125, 250, 250, 250, 250]

Answer: assert Solution().gcdValues(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, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99], queries = [0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250, 260, 270, 280, 290, 300, 310, 320, 330, 340, 350, 360, 370, 380, 390, 400, 410, 420, 430, 440, 450, 460, 470, 480, 490, 500, 510, 520, 530, 540, 550, 560, 570, 580, 590, 600, 610, 620, 630, 640, 650, 660, 670, 680, 690, 700]) == [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, 1, 1, 1, 1, 1, 1, 1, 1, 1]

Answer: assert Solution().gcdValues(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000], queries = [0, 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, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49]) == [100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 200, 200, 200, 200, 200, 200, 200, 200, 200, 300, 300, 300, 400, 500, 1001, 1001, 1001, 1001, 1001]

Answer: assert Solution().gcdValues(nums = [101, 202, 303, 404, 505, 606, 707, 808, 909, 1010], queries = [0,45,90,135,180,225,269]) == [101, 1011, 1011, 1011, 1011, 1011, 1011]

Answer: assert Solution().gcdValues(nums = [3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101], queries = [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49]) == [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]

Answer: assert Solution().gcdValues(nums = [99999, 99998, 99997, 99996, 99995, 99994, 99993, 99992, 99991, 99990], queries = [0, 44, 45, 46, 47, 48]) == [1, 9, 100000, 100000, 100000, 100000]

Answer: assert Solution().gcdValues(nums = [100,200,300,400,500,600,700,800,900,1000], queries = [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49]) == [100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 200, 200, 200, 200, 200, 200, 200, 200, 200, 300, 300, 300, 400, 500, 1001, 1001, 1001, 1001, 1001]

Answer: assert Solution().gcdValues(nums = [1234, 2345, 3456, 4567, 5678, 6789, 7890, 8901, 9012, 1011], queries = [0, 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, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 6, 6, 9, 12, 9013]

Answer: assert Solution().gcdValues(nums = [1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29], queries = [0, 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, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49]) == [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]

Answer: assert Solution().gcdValues(nums = [50000,40000,30000,20000,10000], queries = [0,1,2,3,4,5,6,7,8,9]) == [10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 20000]

Answer: assert Solution().gcdValues(nums = [8,16,24,32,40,48,56,64,72,80,88,96,104,112,120,128,136,144,152,160], queries = [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99]) == [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]

Answer: assert Solution().gcdValues(nums = [42, 63, 84, 105, 126, 147, 168, 189, 210, 231, 252], queries = [0, 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]) == [21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21]

Answer: assert Solution().gcdValues(nums = [50000, 100000, 150000, 200000, 250000, 300000, 350000, 400000, 450000, 500000], queries = [0, 4, 9, 14, 19, 24, 29, 34, 39, 44]) == [50000, 50000, 50000, 50000, 50000, 50000, 50000, 100000, 100000, 250000]

Answer: assert Solution().gcdValues(nums = [50000, 25000, 12500, 6250, 3125, 1562, 781, 390, 195, 97], queries = [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

Answer: assert Solution().gcdValues(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30], queries = [0, 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]) == [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]

Answer: assert Solution().gcdValues(nums = [9, 18, 27, 36, 45, 54, 63, 72, 81, 90], queries = [0, 40, 45, 50, 55]) == [9, 27, 91, 91, 91]

Answer: assert Solution().gcdValues(nums = [3,6,9,12,15,18,21,24,27,30], queries = [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]) == [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]

Answer: assert Solution().gcdValues(nums = [12, 18, 24, 30, 36, 42, 48, 54, 60], queries = [0, 10, 20, 30, 40]) == [6, 6, 6, 12, 61]

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

Answer: assert Solution().gcdValues(nums = [2, 4, 8, 16, 32, 64, 128, 256, 512, 1024], queries = [0, 44, 45, 46, 47, 48]) == [2, 512, 1025, 1025, 1025, 1025]

Answer: assert Solution().gcdValues(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], queries = [0, 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, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]) == [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]

Answer: assert Solution().gcdValues(nums = [1,2,3,4,5,6,7,8,9,10], queries = [0,10,20,30,40,44]) == [1, 1, 1, 1, 3, 5]

Answer: assert Solution().gcdValues(nums = [10000, 20000, 30000, 40000, 50000], queries = [0,9,18,26]) == [10000, 20000, 50001, 50001]

Answer: assert Solution().gcdValues(nums = [17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204], queries = [0, 54, 60, 65, 70]) == [17, 34, 51, 102, 205]

Answer: assert Solution().gcdValues(nums = [123, 246, 369, 492, 615, 738, 861, 984, 1107, 1230], queries = [0, 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, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49]) == [123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 246, 246, 246, 246, 246, 246, 246, 246, 246, 369, 369, 369, 492, 615, 1231, 1231, 1231, 1231, 1231]

Answer: assert Solution().gcdValues(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100], queries = [0, 170, 180, 190, 200]) == [5, 20, 25, 101, 101]

Answer: assert Solution().gcdValues(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], queries = [0, 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, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]) == [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, 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]

Answer: assert Solution().gcdValues(nums = [3, 6, 9, 12, 15, 18], queries = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]) == [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 9]

Answer: assert Solution().gcdValues(nums = [500, 1000, 1500, 2000, 2500], queries = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [500, 500, 500, 500, 500, 500, 500, 500, 500, 1000, 2501]

Answer: assert Solution().gcdValues(nums = [40000, 40001, 40002, 40003, 40004, 40005, 40006, 40007, 40008, 40009], queries = [0, 44, 45, 46, 47, 48]) == [1, 8, 40010, 40010, 40010, 40010]

Answer: assert Solution().gcdValues(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], queries = [0, 44, 45, 46, 47, 48]) == [1, 5, 11, 11, 11, 11]

Answer: assert Solution().gcdValues(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30], queries = [0, 44, 45, 46, 47, 48]) == [3, 15, 31, 31, 31, 31]

Answer: assert Solution().gcdValues(nums = [3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409], queries = [0, 100, 200, 300, 400, 499]) == [1, 1, 1, 1, 1, 1]

Answer: assert Solution().gcdValues(nums = [50000, 40000, 30000, 20000, 10000], queries = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == [10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 20000]

Answer: assert Solution().gcdValues(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], queries = [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59]) == [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]

Answer: assert Solution().gcdValues(nums = [50000, 25000, 12500, 6250, 3125, 1562, 781, 390, 195, 97, 48, 24, 12, 6, 3, 1], queries = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

Answer: assert Solution().gcdValues(nums = [12, 18, 24, 30, 36, 42], queries = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 12, 18, 43]

Answer: assert Solution().gcdValues(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500], queries = [0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140]) == [100, 100, 100, 100, 100, 100, 100, 100, 200, 300, 500, 1501, 1501, 1501, 1501]

Answer: assert Solution().gcdValues(nums = [8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60], queries = [0, 5, 10, 15, 20, 25, 30, 35, 40, 45]) == [4, 4, 4, 4, 4, 4, 4, 4, 4, 4]

Answer: assert Solution().gcdValues(nums = [8, 16, 24, 32, 40, 48, 56, 64], queries = [0, 5, 10, 15, 20, 25, 30, 35, 40, 41, 42, 43, 44, 45, 46, 47, 48]) == [8, 8, 8, 8, 8, 16, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65]

Answer: assert Solution().gcdValues(nums = [50000, 25000, 12500, 6250, 3125, 1562, 781, 390, 195, 97], queries = [0, 44, 45, 46, 47, 48]) == [1, 25000, 50001, 50001, 50001, 50001]

Answer: assert Solution().gcdValues(nums = [101, 103, 107, 109, 113, 127, 131, 137, 139, 149], queries = [0, 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, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49]) == [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, 150, 150, 150, 150, 150]

Answer: assert Solution().gcdValues(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], queries = [0, 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, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49]) == [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 20, 20, 20, 20, 20, 20, 20, 20, 20, 30, 30, 30, 40, 50, 101, 101, 101, 101, 101]

Answer: assert Solution().gcdValues(nums = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29], queries = [0, 44, 45, 46, 47, 48]) == [1, 1, 30, 30, 30, 30]

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

Answer: assert Solution().gcdValues(nums = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97], queries = [0, 100, 200, 300, 400, 500, 600, 700, 800, 900]) == [1, 1, 1, 98, 98, 98, 98, 98, 98, 98]

Answer: assert Solution().gcdValues(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], queries = [0, 10, 20, 30, 40, 50, 60, 70, 80, 90]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

Answer: assert Solution().gcdValues(nums = [23, 46, 69, 92, 115, 138, 161, 184, 207, 230], queries = [0, 5, 10, 15, 20, 25, 30, 35, 40, 45]) == [23, 23, 23, 23, 23, 23, 23, 46, 69, 231]

Answer: assert Solution().gcdValues(nums = [8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96], queries = [0, 54, 60, 65, 70]) == [8, 16, 24, 48, 97]

Answer: assert Solution().gcdValues(nums = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71], queries = [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49]) == [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]

Answer: assert Solution().gcdValues(nums = [11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 220], queries = [0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95]) == [11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11]

Answer: assert Solution().gcdValues(nums = [10000, 10000, 10000, 10000, 10000], queries = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10001]

Answer: assert Solution().gcdValues(nums = [100, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600], queries = [0,45,90,135,180,225,269]) == [50, 150, 601, 601, 601, 601, 601]

Answer: assert Solution().gcdValues(nums = [10000, 5000, 2500, 1250, 625, 312, 156], queries = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]) == [1, 1, 2, 2, 4, 4, 4, 4, 8, 8, 156, 625, 625, 625, 625, 1250, 1250]

Answer: assert Solution().gcdValues(nums = [11, 22, 33, 44, 55, 66, 77, 88, 99, 110], queries = [0, 40, 55, 65, 70]) == [11, 33, 111, 111, 111]

Answer: assert Solution().gcdValues(nums = [10000, 20000, 30000, 40000, 50000], queries = [0, 4, 7, 9, 10]) == [10000, 10000, 10000, 20000, 50001]

Answer: assert Solution().gcdValues(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30], queries = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]) == [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]

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

Answer: assert Solution().gcdValues(nums = [42, 56, 70, 84, 98, 112, 126, 140], queries = [0, 16, 24, 28, 32]) == [14, 14, 42, 141, 141]

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

Answer: assert Solution().gcdValues(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45], queries = [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44]) == [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]

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 gcdValues(self, nums: List[int], queries: List[int]) -> List[int]:
        mx = max(nums)
        cnt = Counter(nums)
        cnt_g = [0] * (mx + 1)
        for i in range(mx, 0, -1):
            v = 0
            for j in range(i, mx + 1, i):
                v += cnt[j]
                cnt_g[i] -= cnt_g[j]
            cnt_g[i] += v * (v - 1) // 2
        s = list(accumulate(cnt_g))
        return [bisect_right(s, q) for q in queries]


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:
There exists an undirected tree with n nodes numbered 0 to n - 1. You are given a 2D integer array edges of length n - 1, where edges[i] = [ui, vi] indicates that there is an edge between nodes ui and vi in the tree.
Initially, all nodes are unmarked. After every second, you mark all unmarked nodes which have at least one marked node adjacent to them.
Return an array nodes where nodes[i] is the last node to get marked in the tree, if you mark node i at time t = 0. If nodes[i] has multiple answers for any node i, you can choose any one answer.

Example 1:

Input: edges = [[0,1],[0,2]]
Output: [2,2,1]
Explanation:

For i = 0, the nodes are marked in the sequence: [0] -> [0,1,2]. Either 1 or 2 can be the answer.
For i = 1, the nodes are marked in the sequence: [1] -> [0,1] -> [0,1,2]. Node 2 is marked last.
For i = 2, the nodes are marked in the sequence: [2] -> [0,2] -> [0,1,2]. Node 1 is marked last.

Example 2:

Input: edges = [[0,1]]
Output: [1,0]
Explanation:

For i = 0, the nodes are marked in the sequence: [0] -> [0,1].
For i = 1, the nodes are marked in the sequence: [1] -> [0,1].

Example 3:

Input: edges = [[0,1],[0,2],[2,3],[2,4]]
Output: [3,3,1,1,1]
Explanation:

For i = 0, the nodes are marked in the sequence: [0] -> [0,1,2] -> [0,1,2,3,4].
For i = 1, the nodes are marked in the sequence: [1] -> [0,1] -> [0,1,2] -> [0,1,2,3,4].
For i = 2, the nodes are marked in the sequence: [2] -> [0,2,3,4] -> [0,1,2,3,4].
For i = 3, the nodes are marked in the sequence: [3] -> [2,3] -> [0,2,3,4] -> [0,1,2,3,4].
For i = 4, the nodes are marked in the sequence: [4] -> [2,4] -> [0,2,3,4] -> [0,1,2,3,4].

Constraints:

2 <= n <= 105
edges.length == n - 1
edges[i].length == 2
0 <= edges[i][0], edges[i][1] <= n - 1
The input is generated such that edges represents a valid tree.

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

SOLUTION:

Question:
PROBLEM:
There exists an undirected tree with n nodes numbered 0 to n - 1. You are given a 2D integer array edges of length n - 1, where edges[i] = [ui, vi] indicates that there is an edge between nodes ui and vi in the tree.
Initially, all nodes are unmarked. After every second, you mark all unmarked nodes which have at least one marked node adjacent to them.
Return an array nodes where nodes[i] is the last node to get marked in the tree, if you mark node i at time t = 0. If nodes[i] has multiple answers for any node i, you can choose any one answer.

Example 1:

Input: edges = [[0,1],[0,2]]
Output: [2,2,1]
Explanation:

For i = 0, the nodes are marked in the sequence: [0] -> [0,1,2]. Either 1 or 2 can be the answer.
For i = 1, the nodes are marked in the sequence: [1] -> [0,1] -> [0,1,2]. Node 2 is marked last.
For i = 2, the nodes are marked in the sequence: [2] -> [0,2] -> [0,1,2]. Node 1 is marked last.

Example 2:

Input: edges = [[0,1]]
Output: [1,0]
Explanation:

For i = 0, the nodes are marked in the sequence: [0] -> [0,1].
For i = 1, the nodes are marked in the sequence: [1] -> [0,1].

Example 3:

Input: edges = [[0,1],[0,2],[2,3],[2,4]]
Output: [3,3,1,1,1]
Explanation:

For i = 0, the nodes are marked in the sequence: [0] -> [0,1,2] -> [0,1,2,3,4].
For i = 1, the nodes are marked in the sequence: [1] -> [0,1] -> [0,1,2] -> [0,1,2,3,4].
For i = 2, the nodes are marked in the sequence: [2] -> [0,2,3,4] -> [0,1,2,3,4].
For i = 3, the nodes are marked in the sequence: [3] -> [2,3] -> [0,2,3,4] -> [0,1,2,3,4].
For i = 4, the nodes are marked in the sequence: [4] -> [2,4] -> [0,2,3,4] -> [0,1,2,3,4].

Constraints:

2 <= n <= 105
edges.length == n - 1
edges[i].length == 2
0 <= edges[i][0], edges[i][1] <= n - 1
The input is generated such that edges represents a valid tree.

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

SOLUTION:

assert Solution().lastMarkedNodes(edges = [[0,1],[0,2]]) == [2, 2, 1]

assert Solution().lastMarkedNodes(edges = [[0,1]]) == [1, 0]

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[0,2]]) == [2, 2, 1]

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[0,2],[2,3],[2,4]]) == [3, 3, 1, 1, 1]

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[1,2],[1,3],[3,4],[3,5],[5,6]]) == [6, 6, 6, 0, 0, 0, 0]

Answer: assert Solution().lastMarkedNodes(edges = [[0,1]]) == [1, 0]

Answer: assert Solution().lastMarkedNodes(edges = [[0,2],[0,3],[1,2]]) == [1, 3, 3, 1]

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[0,2],[2,3],[2,4],[2,5],[5,6]]) == [6, 6, 1, 1, 1, 1, 1]

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[1,2],[2,3],[3,4],[2,5],[5,6]]) == [4, 4, 0, 0, 0, 0, 0]

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]]) == [5, 5, 3, 5, 5, 3, 3]

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

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[1,2],[2,3],[3,4],[4,5]]) == [5, 5, 5, 0, 0, 0]

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[1,2],[1,3],[3,4],[3,5],[3,6]]) == [4, 4, 4, 0, 0, 0, 0]

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[0,2],[2,3],[2,4],[4,5],[4,6],[4,7],[5,8],[5,9],[6,10],[6,11],[7,12],[7,13]]) == [8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

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

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[0,2],[0,3],[1,4],[1,5],[2,6],[2,7],[3,8],[3,9],[4,10],[4,11],[5,12],[5,13],[6,14],[6,15],[7,16],[7,17]]) == [14, 14, 10, 14, 14, 14, 10, 10, 14, 14, 14, 14, 14, 14, 10, 10, 10, 10]

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6],[3,7],[3,8],[4,9],[4,10],[5,11],[5,12],[6,13],[6,14],[7,15],[7,16],[8,17],[8,18],[9,19],[9,20],[10,21],[10,22],[11,23],[11,24],[12,25],[12,26],[13,27],[13,28],[14,29],[14,30]]) == [23, 23, 15, 23, 23, 15, 15, 23, 23, 23, 23, 15, 15, 15, 15, 23, 23, 23, 23, 23, 23, 23, 23, 15, 15, 15, 15, 15, 15, 15, 15]

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

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[0,2],[1,3],[2,4],[3,5],[3,6],[4,7],[4,8],[5,9],[5,10],[6,11],[6,12],[7,13],[7,14],[8,15],[8,16],[9,17],[9,18],[10,19],[10,20],[11,21],[11,22],[12,23],[12,24],[13,25],[13,26],[14,27],[14,28],[15,29],[15,30],[16,31],[16,32],[17,33],[17,34],[18,35],[18,36],[19,37],[19,38],[20,39],[20,40],[21,41],[21,42],[22,43],[22,44],[23,45],[23,46],[24,47],[24,48]]) == [33, 25, 33, 25, 33, 25, 25, 33, 33, 25, 25, 25, 25, 33, 33, 33, 33, 25, 25, 25, 25, 25, 25, 25, 25, 33, 33, 33, 33, 33, 33, 33, 33, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25]

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[0,2],[2,3],[2,4],[2,5],[5,6],[5,7],[4,8],[4,9],[3,10],[3,11],[11,12],[11,13],[13,14],[13,15],[15,16]]) == [16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 1, 1, 1, 1, 1, 1]

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

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

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[1,2],[1,3],[2,4],[3,5],[4,6],[4,7],[5,8],[5,9],[6,10],[6,11],[7,12],[7,13]]) == [10, 10, 8, 10, 8, 10, 8, 8, 10, 10, 8, 8, 8, 8]

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[1,2],[1,3],[2,4],[2,5],[2,6],[3,7],[3,8],[3,9],[4,10],[4,11],[4,12],[5,13],[5,14],[5,15],[6,16],[6,17],[6,18],[7,19],[7,20],[7,21]]) == [19, 19, 19, 10, 19, 19, 19, 10, 10, 10, 19, 19, 19, 19, 19, 19, 19, 19, 19, 10, 10, 10]

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20],[20,21],[21,22],[22,23],[23,24],[24,25],[25,26],[26,27],[27,28],[28,29]]) == [29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[1,2],[1,3],[2,4],[2,5],[3,6],[3,7],[4,8],[4,9],[5,10],[5,11]]) == [8, 8, 6, 8, 6, 6, 8, 8, 6, 6, 6, 6]

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

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

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

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20],[0,21],[21,22],[22,23],[23,24],[24,25],[25,26],[26,27],[27,28],[28,29],[29,30],[30,31]]) == [20, 20, 20, 20, 20, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20]

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

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

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[5,6],[6,7],[6,8],[7,9],[8,10],[10,11]]) == [11, 11, 11, 11, 11, 3, 3, 3, 3, 3, 3, 3]

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

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[1,2],[1,3],[3,4],[3,5],[2,6],[2,7],[6,8],[6,9],[8,10],[8,11],[9,12],[9,13]]) == [10, 10, 4, 10, 10, 10, 4, 4, 4, 4, 4, 4, 4, 4]

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

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

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

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

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

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

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

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[0,12],[12,13],[13,14],[14,15],[15,16]]) == [11, 11, 11, 16, 16, 16, 16, 16, 16, 16, 16, 16, 11, 11, 11, 11, 11]

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

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6],[3,7],[3,8],[4,9],[4,10],[5,11],[5,12],[6,13],[6,14],[7,15],[7,16],[8,17],[8,18],[9,19],[9,20],[10,21],[10,22],[11,23],[11,24],[12,25],[12,26]]) == [23, 23, 15, 23, 23, 15, 15, 23, 23, 23, 23, 15, 15, 15, 15, 23, 23, 23, 23, 23, 23, 23, 23, 15, 15, 15, 15]

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20],[20,21],[21,22],[22,23],[23,24],[24,25]]) == [25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6],[3,7],[3,8],[4,9],[4,10],[5,11],[5,12],[6,13],[6,14],[7,15],[7,16],[8,17],[8,18],[9,19],[9,20],[10,21],[10,22]]) == [15, 11, 15, 11, 11, 15, 15, 11, 11, 11, 11, 15, 15, 15, 15, 11, 11, 11, 11, 11, 11, 11, 11]

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

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6],[3,7],[3,8],[4,9],[4,10],[5,11],[5,12],[6,13],[6,14],[7,15],[7,16],[8,17],[8,18],[9,19],[9,20],[10,21],[10,22],[11,23],[11,24],[12,25],[12,26],[13,27],[13,28],[14,29],[14,30],[15,31],[15,32],[16,33],[16,34],[17,35],[17,36],[18,37],[18,38],[19,39],[19,40],[20,41],[20,42],[21,43],[21,44],[22,45],[22,46],[23,47],[23,48],[24,49],[24,50]]) == [47, 47, 31, 47, 47, 31, 31, 47, 47, 47, 47, 31, 31, 31, 31, 47, 47, 47, 47, 47, 47, 47, 47, 31, 31, 31, 31, 31, 31, 31, 31, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 31, 31, 31, 31]

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6],[3,7],[3,8],[4,9],[5,10],[5,11],[6,12],[6,13]]) == [10, 10, 7, 10, 10, 7, 7, 10, 10, 10, 7, 7, 7, 7]

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[0,2],[0,3],[1,4],[1,5],[1,6],[2,7],[2,8],[2,9],[3,10],[3,11],[3,12],[4,13],[4,14],[4,15],[5,16],[5,17],[5,18],[6,19],[6,20],[6,21],[7,22],[7,23],[7,24],[8,25],[8,26],[8,27],[9,28],[9,29],[9,30]]) == [22, 22, 13, 22, 22, 22, 22, 13, 13, 13, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 13, 13, 13, 13, 13, 13, 13, 13, 13]

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

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

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

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

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[1,2],[1,3],[1,4],[2,5],[2,6],[2,7],[3,8],[3,9],[3,10],[4,11],[4,12],[4,13]]) == [8, 8, 8, 5, 8, 8, 8, 8, 5, 5, 5, 8, 8, 8]

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

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13]]) == [13, 13, 13, 13, 13, 13, 13, 0, 0, 0, 0, 0, 0, 0]

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

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

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

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[1,2],[1,3],[2,4],[2,5],[3,6],[3,7],[4,8],[4,9],[5,10],[5,11],[6,12],[6,13],[7,14],[7,15],[8,16],[8,17],[9,18],[9,19],[10,20],[10,21],[11,22],[11,23],[12,24],[12,25],[13,26],[13,27],[14,28],[14,29],[15,30],[15,31]]) == [24, 24, 24, 16, 24, 24, 16, 16, 24, 24, 24, 24, 16, 16, 16, 16, 24, 24, 24, 24, 24, 24, 24, 24, 16, 16, 16, 16, 16, 16, 16, 16]

Answer: assert Solution().lastMarkedNodes(edges = [[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20],[20,21],[21,22],[22,23],[23,24]]) == [24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

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

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 lastMarkedNodes(self, edges: List[List[int]]) -> List[int]:
        def dfs(i: int, fa: int, dist: List[int]):
            for j in g[i]:
                if j != fa:
                    dist[j] = dist[i] + 1
                    dfs(j, i, dist)

        n = len(edges) + 1
        g = [[] for _ in range(n)]
        for u, v in edges:
            g[u].append(v)
            g[v].append(u)

        dist1 = [-1] * n
        dist1[0] = 0
        dfs(0, -1, dist1)
        a = dist1.index(max(dist1))

        dist2 = [-1] * n
        dist2[a] = 0
        dfs(a, -1, dist2)
        b = dist2.index(max(dist2))

        dist3 = [-1] * n
        dist3[b] = 0
        dfs(b, -1, dist3)

        return [a if x > y else b for x, y in zip(dist2, dist3)]


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 array nums consisting of n prime integers.
You need to construct an array ans of length n, such that, for each index i, the bitwise OR of ans[i] and ans[i] + 1 is equal to nums[i], i.e. ans[i] OR (ans[i] + 1) == nums[i].
Additionally, you must minimize each value of ans[i] in the resulting array.
If it is not possible to find such a value for ans[i] that satisfies the condition, then set ans[i] = -1.

Example 1:

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

For i = 0, as there is no value for ans[0] that satisfies ans[0] OR (ans[0] + 1) = 2, so ans[0] = -1.
For i = 1, the smallest ans[1] that satisfies ans[1] OR (ans[1] + 1) = 3 is 1, because 1 OR (1 + 1) = 3.
For i = 2, the smallest ans[2] that satisfies ans[2] OR (ans[2] + 1) = 5 is 4, because 4 OR (4 + 1) = 5.
For i = 3, the smallest ans[3] that satisfies ans[3] OR (ans[3] + 1) = 7 is 3, because 3 OR (3 + 1) = 7.

Example 2:

Input: nums = [11,13,31]
Output: [9,12,15]
Explanation:

For i = 0, the smallest ans[0] that satisfies ans[0] OR (ans[0] + 1) = 11 is 9, because 9 OR (9 + 1) = 11.
For i = 1, the smallest ans[1] that satisfies ans[1] OR (ans[1] + 1) = 13 is 12, because 12 OR (12 + 1) = 13.
For i = 2, the smallest ans[2] that satisfies ans[2] OR (ans[2] + 1) = 31 is 15, because 15 OR (15 + 1) = 31.

Constraints:

1 <= nums.length <= 100
2 <= nums[i] <= 109
nums[i] is a prime number.

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

SOLUTION:

Question:
PROBLEM:
You are given an array nums consisting of n prime integers.
You need to construct an array ans of length n, such that, for each index i, the bitwise OR of ans[i] and ans[i] + 1 is equal to nums[i], i.e. ans[i] OR (ans[i] + 1) == nums[i].
Additionally, you must minimize each value of ans[i] in the resulting array.
If it is not possible to find such a value for ans[i] that satisfies the condition, then set ans[i] = -1.

Example 1:

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

For i = 0, as there is no value for ans[0] that satisfies ans[0] OR (ans[0] + 1) = 2, so ans[0] = -1.
For i = 1, the smallest ans[1] that satisfies ans[1] OR (ans[1] + 1) = 3 is 1, because 1 OR (1 + 1) = 3.
For i = 2, the smallest ans[2] that satisfies ans[2] OR (ans[2] + 1) = 5 is 4, because 4 OR (4 + 1) = 5.
For i = 3, the smallest ans[3] that satisfies ans[3] OR (ans[3] + 1) = 7 is 3, because 3 OR (3 + 1) = 7.

Example 2:

Input: nums = [11,13,31]
Output: [9,12,15]
Explanation:

For i = 0, the smallest ans[0] that satisfies ans[0] OR (ans[0] + 1) = 11 is 9, because 9 OR (9 + 1) = 11.
For i = 1, the smallest ans[1] that satisfies ans[1] OR (ans[1] + 1) = 13 is 12, because 12 OR (12 + 1) = 13.
For i = 2, the smallest ans[2] that satisfies ans[2] OR (ans[2] + 1) = 31 is 15, because 15 OR (15 + 1) = 31.

Constraints:

1 <= nums.length <= 100
2 <= nums[i] <= 109
nums[i] is a prime number.

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

SOLUTION:

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

assert Solution().minBitwiseArray(nums = [11,13,31]) == [9, 12, 15]

assert Solution().minBitwiseArray(nums = [29,101,137]) == [28, 100, 136]

assert Solution().minBitwiseArray(nums = [17,19,23]) == [16, 17, 19]

assert Solution().minBitwiseArray(nums = [29,37,41]) == [28, 36, 40]

assert Solution().minBitwiseArray(nums = [43,47,53]) == [41, 39, 52]

assert Solution().minBitwiseArray(nums = [3,17,79]) == [1, 16, 71]

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

assert Solution().minBitwiseArray(nums = [2, 17, 19, 23]) == [-1, 16, 17, 19]

Answer: assert Solution().minBitwiseArray(nums = [41,43,47,53]) == [40, 41, 39, 52]

Answer: assert Solution().minBitwiseArray(nums = [29, 37, 41, 43]) == [28, 36, 40, 41]

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

Answer: assert Solution().minBitwiseArray(nums = [11,13,31]) == [9, 12, 15]

Answer: assert Solution().minBitwiseArray(nums = [29,101,137]) == [28, 100, 136]

Answer: assert Solution().minBitwiseArray(nums = [17,19,23]) == [16, 17, 19]

Answer: assert Solution().minBitwiseArray(nums = [53, 59, 61, 67]) == [52, 57, 60, 65]

Answer: assert Solution().minBitwiseArray(nums = [29,37,41]) == [28, 36, 40]

Answer: assert Solution().minBitwiseArray(nums = [43,47,53]) == [41, 39, 52]

Answer: assert Solution().minBitwiseArray(nums = [3,17,79]) == [1, 16, 71]

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

Answer: assert Solution().minBitwiseArray(nums = [59,61,67,71]) == [57, 60, 65, 67]

Answer: assert Solution().minBitwiseArray(nums = [2, 17, 19, 23]) == [-1, 16, 17, 19]

Answer: assert Solution().minBitwiseArray(nums = [17,19,23,29]) == [16, 17, 19, 28]

Answer: assert Solution().minBitwiseArray(nums = [3163, 3167, 3169, 3181]) == [3161, 3151, 3168, 3180]

Answer: assert Solution().minBitwiseArray(nums = [877, 881, 883, 887]) == [876, 880, 881, 883]

Answer: assert Solution().minBitwiseArray(nums = [83, 89, 97, 101, 103, 107, 109]) == [81, 88, 96, 100, 99, 105, 108]

Answer: assert Solution().minBitwiseArray(nums = [1613, 1619, 1621, 1627]) == [1612, 1617, 1620, 1625]

Answer: assert Solution().minBitwiseArray(nums = [1319, 1321, 1327, 1361]) == [1315, 1320, 1319, 1360]

Answer: assert Solution().minBitwiseArray(nums = [107, 109, 113, 127]) == [105, 108, 112, 63]

Answer: assert Solution().minBitwiseArray(nums = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499]) == [-1, 1, 4, 3, 9, 12, 16, 17, 19, 28, 15, 36, 40, 41, 39, 52, 57, 60, 65, 67, 72, 71, 81, 88, 96, 100, 99, 105, 108, 112, 63, 129, 136, 137, 148, 147, 156, 161, 163, 172, 177, 180, 159, 192, 196, 195, 209, 207, 225, 228, 232, 231, 240, 249, 256, 259, 268, 263, 276, 280, 281, 292, 305, 307, 312, 316, 329, 336, 345, 348, 352, 355, 359, 372, 377, 319, 388, 396, 400, 408, 417, 420, 423, 432, 435, 441, 448, 456, 460, 455, 465, 463, 483, 489, 497]

Answer: assert Solution().minBitwiseArray(nums = [173, 179, 181, 191, 193, 197, 199, 211, 223, 227]) == [172, 177, 180, 159, 192, 196, 195, 209, 207, 225]

Answer: assert Solution().minBitwiseArray(nums = [503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619]) == [499, 508, 520, 521, 540, 545, 556, 561, 568, 569, 576, 585, 592, 595, 600, 591, 612, 616, 617]

Answer: assert Solution().minBitwiseArray(nums = [331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397]) == [329, 336, 345, 348, 352, 355, 359, 372, 377, 319, 388, 396]

Answer: assert Solution().minBitwiseArray(nums = [3299, 3301, 3307, 3313]) == [3297, 3300, 3305, 3312]

Answer: assert Solution().minBitwiseArray(nums = [2711, 2713, 2719, 2729]) == [2707, 2712, 2703, 2728]

Answer: assert Solution().minBitwiseArray(nums = [3889, 3907, 3911, 3917]) == [3888, 3905, 3907, 3916]

Answer: assert Solution().minBitwiseArray(nums = [83, 89, 97, 101]) == [81, 88, 96, 100]

Answer: assert Solution().minBitwiseArray(nums = [827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907]) == [825, 828, 835, 852, 856, 857, 847, 876, 880, 881, 883, 905]

Answer: assert Solution().minBitwiseArray(nums = [281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349]) == [280, 281, 292, 305, 307, 312, 316, 329, 336, 345, 348]

Answer: assert Solution().minBitwiseArray(nums = [2141, 2143, 2153, 2161]) == [2140, 2127, 2152, 2160]

Answer: assert Solution().minBitwiseArray(nums = [503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719]) == [499, 508, 520, 521, 540, 545, 556, 561, 568, 569, 576, 585, 592, 595, 600, 591, 612, 616, 617, 627, 640, 641, 643, 652, 657, 660, 672, 676, 681, 689, 700, 708, 711]

Answer: assert Solution().minBitwiseArray(nums = [3691, 3697, 3701, 3709]) == [3689, 3696, 3700, 3708]

Answer: assert Solution().minBitwiseArray(nums = [659, 673, 683, 701, 709, 719, 733, 739, 743]) == [657, 672, 681, 700, 708, 711, 732, 737, 739]

Answer: assert Solution().minBitwiseArray(nums = [269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331]) == [268, 263, 276, 280, 281, 292, 305, 307, 312, 316, 329]

Answer: assert Solution().minBitwiseArray(nums = [499, 503, 509, 521]) == [497, 499, 508, 520]

Answer: assert Solution().minBitwiseArray(nums = [491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599]) == [489, 497, 499, 508, 520, 521, 540, 545, 556, 561, 568, 569, 576, 585, 592, 595]

Answer: assert Solution().minBitwiseArray(nums = [601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719]) == [600, 591, 612, 616, 617, 627, 640, 641, 643, 652, 657, 660, 672, 676, 681, 689, 700, 708, 711]

Answer: assert Solution().minBitwiseArray(nums = [3319, 3323, 3329, 3331]) == [3315, 3321, 3328, 3329]

Answer: assert Solution().minBitwiseArray(nums = [1237, 1249, 1259, 1277]) == [1236, 1248, 1257, 1276]

Answer: assert Solution().minBitwiseArray(nums = [131, 137, 139, 149, 151, 157]) == [129, 136, 137, 148, 147, 156]

Answer: assert Solution().minBitwiseArray(nums = [431, 433, 439, 443]) == [423, 432, 435, 441]

Answer: assert Solution().minBitwiseArray(nums = [3853, 3863, 3877, 3881]) == [3852, 3859, 3876, 3880]

Answer: assert Solution().minBitwiseArray(nums = [907, 911, 919, 929]) == [905, 903, 915, 928]

Answer: assert Solution().minBitwiseArray(nums = [431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499]) == [423, 432, 435, 441, 448, 456, 460, 455, 465, 463, 483, 489, 497]

Answer: assert Solution().minBitwiseArray(nums = [739, 743, 751, 757]) == [737, 739, 743, 756]

Answer: assert Solution().minBitwiseArray(nums = [3761, 3767, 3769, 3779]) == [3760, 3763, 3768, 3777]

Answer: assert Solution().minBitwiseArray(nums = [503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601]) == [499, 508, 520, 521, 540, 545, 556, 561, 568, 569, 576, 585, 592, 595, 600]

Answer: assert Solution().minBitwiseArray(nums = [3823, 3833, 3847, 3851]) == [3815, 3832, 3843, 3849]

Answer: assert Solution().minBitwiseArray(nums = [523, 541, 547, 557]) == [521, 540, 545, 556]

Answer: assert Solution().minBitwiseArray(nums = [547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647]) == [545, 556, 561, 568, 569, 576, 585, 592, 595, 600, 591, 612, 616, 617, 627, 640, 641, 643]

Answer: assert Solution().minBitwiseArray(nums = [293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379]) == [292, 305, 307, 312, 316, 329, 336, 345, 348, 352, 355, 359, 372, 377]

Answer: assert Solution().minBitwiseArray(nums = [449, 457, 461, 463]) == [448, 456, 460, 455]

Answer: assert Solution().minBitwiseArray(nums = [761, 769, 773, 787]) == [760, 768, 772, 785]

Answer: assert Solution().minBitwiseArray(nums = [1933, 1949, 1951, 1973]) == [1932, 1948, 1935, 1972]

Answer: assert Solution().minBitwiseArray(nums = [379, 383, 389, 397]) == [377, 319, 388, 396]

Answer: assert Solution().minBitwiseArray(nums = [1901, 1907, 1913, 1931]) == [1900, 1905, 1912, 1929]

Answer: assert Solution().minBitwiseArray(nums = [3371, 3373, 3389, 3391]) == [3369, 3372, 3388, 3359]

Answer: assert Solution().minBitwiseArray(nums = [1117, 1123, 1129, 1151]) == [1116, 1121, 1128, 1087]

Answer: assert Solution().minBitwiseArray(nums = [2963, 2969, 2971, 2999]) == [2961, 2968, 2969, 2995]

Answer: assert Solution().minBitwiseArray(nums = [1367, 1373, 1381, 1399]) == [1363, 1372, 1380, 1395]

Answer: assert Solution().minBitwiseArray(nums = [3659, 3671, 3673, 3677]) == [3657, 3667, 3672, 3676]

Answer: assert Solution().minBitwiseArray(nums = [1187, 1193, 1201, 1213]) == [1185, 1192, 1200, 1212]

Answer: assert Solution().minBitwiseArray(nums = [2797, 2801, 2803, 2819]) == [2796, 2800, 2801, 2817]

Answer: assert Solution().minBitwiseArray(nums = [2689, 2693, 2699, 2707]) == [2688, 2692, 2697, 2705]

Answer: assert Solution().minBitwiseArray(nums = [353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421]) == [352, 355, 359, 372, 377, 319, 388, 396, 400, 408, 417, 420]

Answer: assert Solution().minBitwiseArray(nums = [163, 167, 173, 179, 181, 191, 193, 197, 199]) == [161, 163, 172, 177, 180, 159, 192, 196, 195]

Answer: assert Solution().minBitwiseArray(nums = [631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797]) == [627, 640, 641, 643, 652, 657, 660, 672, 676, 681, 689, 700, 708, 711, 723, 732, 737, 739, 743, 756, 760, 768, 772, 785, 796]

Answer: assert Solution().minBitwiseArray(nums = [229, 233, 239, 241, 251, 257, 263, 269, 271, 277]) == [228, 232, 231, 240, 249, 256, 259, 268, 263, 276]

Answer: assert Solution().minBitwiseArray(nums = [3919, 3923, 3929, 3931]) == [3911, 3921, 3928, 3929]

Answer: assert Solution().minBitwiseArray(nums = [2927, 2939, 2953, 2957]) == [2919, 2937, 2952, 2956]

Answer: assert Solution().minBitwiseArray(nums = [419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499]) == [417, 420, 423, 432, 435, 441, 448, 456, 460, 455, 465, 463, 483, 489, 497]

Answer: assert Solution().minBitwiseArray(nums = [3067, 3079, 3083, 3089]) == [3065, 3075, 3081, 3088]

Answer: assert Solution().minBitwiseArray(nums = [607, 613, 617, 619]) == [591, 612, 616, 617]

Answer: assert Solution().minBitwiseArray(nums = [3407, 3413, 3433, 3449]) == [3399, 3412, 3432, 3448]

Answer: assert Solution().minBitwiseArray(nums = [199, 211, 223, 227, 229, 233, 239, 241, 251, 257]) == [195, 209, 207, 225, 228, 232, 231, 240, 249, 256]

Answer: assert Solution().minBitwiseArray(nums = [1279, 1283, 1289, 1291]) == [1151, 1281, 1288, 1289]

Answer: assert Solution().minBitwiseArray(nums = [191, 193, 197, 199]) == [159, 192, 196, 195]

Answer: assert Solution().minBitwiseArray(nums = [1153, 1163, 1171, 1181]) == [1152, 1161, 1169, 1180]

Answer: assert Solution().minBitwiseArray(nums = [163, 167, 173, 179, 181, 191, 193, 197]) == [161, 163, 172, 177, 180, 159, 192, 196]

Answer: assert Solution().minBitwiseArray(nums = [1297, 1301, 1303, 1307]) == [1296, 1300, 1299, 1305]

Answer: assert Solution().minBitwiseArray(nums = [2179, 2203, 2207, 2213]) == [2177, 2201, 2191, 2212]

Answer: assert Solution().minBitwiseArray(nums = [2417, 2423, 2437, 2441]) == [2416, 2419, 2436, 2440]

Answer: assert Solution().minBitwiseArray(nums = [3187, 3191, 3203, 3209]) == [3185, 3187, 3201, 3208]

Answer: assert Solution().minBitwiseArray(nums = [683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821]) == [681, 689, 700, 708, 711, 723, 732, 737, 739, 743, 756, 760, 768, 772, 785, 796, 808, 809, 820]

Answer: assert Solution().minBitwiseArray(nums = [3593, 3607, 3613, 3617]) == [3592, 3603, 3612, 3616]

Answer: assert Solution().minBitwiseArray(nums = [967, 971, 977, 983]) == [963, 969, 976, 979]

Answer: assert Solution().minBitwiseArray(nums = [233, 239, 241, 251, 257, 263, 269, 271, 277, 281]) == [232, 231, 240, 249, 256, 259, 268, 263, 276, 280]

Answer: assert Solution().minBitwiseArray(nums = [359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439]) == [355, 359, 372, 377, 319, 388, 396, 400, 408, 417, 420, 423, 432, 435]

Answer: assert Solution().minBitwiseArray(nums = [2087, 2089, 2099, 2111]) == [2083, 2088, 2097, 2079]

Answer: assert Solution().minBitwiseArray(nums = [569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661]) == [568, 569, 576, 585, 592, 595, 600, 591, 612, 616, 617, 627, 640, 641, 643, 652, 657, 660]

Answer: assert Solution().minBitwiseArray(nums = [337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409]) == [336, 345, 348, 352, 355, 359, 372, 377, 319, 388, 396, 400, 408]

Answer: assert Solution().minBitwiseArray(nums = [3037, 3041, 3049, 3061]) == [3036, 3040, 3048, 3060]

Answer: assert Solution().minBitwiseArray(nums = [277, 281, 283, 293]) == [276, 280, 281, 292]

Answer: assert Solution().minBitwiseArray(nums = [3109, 3119, 3121, 3137]) == [3108, 3111, 3120, 3136]

Answer: assert Solution().minBitwiseArray(nums = [3943, 3947, 3967, 3989]) == [3939, 3945, 3903, 3988]

Answer: assert Solution().minBitwiseArray(nums = [1409, 1423, 1427, 1429]) == [1408, 1415, 1425, 1428]

Answer: assert Solution().minBitwiseArray(nums = [271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359]) == [263, 276, 280, 281, 292, 305, 307, 312, 316, 329, 336, 345, 348, 352, 355]

Answer: assert Solution().minBitwiseArray(nums = [107, 109, 113, 127, 131, 137]) == [105, 108, 112, 63, 129, 136]

Answer: assert Solution().minBitwiseArray(nums = [1847, 1861, 1867, 1871]) == [1843, 1860, 1865, 1863]

Answer: assert Solution().minBitwiseArray(nums = [127, 131, 137, 139]) == [63, 129, 136, 137]

Answer: assert Solution().minBitwiseArray(nums = [383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463]) == [319, 388, 396, 400, 408, 417, 420, 423, 432, 435, 441, 448, 456, 460, 455]

Answer: assert Solution().minBitwiseArray(nums = [3719, 3727, 3733, 3739]) == [3715, 3719, 3732, 3737]

Answer: assert Solution().minBitwiseArray(nums = [2309, 2311, 2333, 2339]) == [2308, 2307, 2332, 2337]

Answer: assert Solution().minBitwiseArray(nums = [3623, 3631, 3637, 3643]) == [3619, 3623, 3636, 3641]

Answer: assert Solution().minBitwiseArray(nums = [719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839]) == [711, 723, 732, 737, 739, 743, 756, 760, 768, 772, 785, 796, 808, 809, 820, 819, 825, 828, 835]

Answer: assert Solution().minBitwiseArray(nums = [1019, 1021, 1031, 1033]) == [1017, 1020, 1027, 1032]

Answer: assert Solution().minBitwiseArray(nums = [103, 107, 109, 113]) == [99, 105, 108, 112]

Answer: assert Solution().minBitwiseArray(nums = [337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401]) == [336, 345, 348, 352, 355, 359, 372, 377, 319, 388, 396, 400]

Answer: assert Solution().minBitwiseArray(nums = [1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093]) == [1008, 1012, 1017, 1020, 1027, 1032, 1031, 1048, 1049, 1060, 1059, 1068, 1055, 1089, 1092]

Answer: assert Solution().minBitwiseArray(nums = [467, 479, 487, 491]) == [465, 463, 483, 489]

Answer: assert Solution().minBitwiseArray(nums = [853, 857, 859, 863]) == [852, 856, 857, 847]

Answer: assert Solution().minBitwiseArray(nums = [2063, 2069, 2081, 2083]) == [2055, 2068, 2080, 2081]

Answer: assert Solution().minBitwiseArray(nums = [2647, 2657, 2659, 2663]) == [2643, 2656, 2657, 2659]

Answer: assert Solution().minBitwiseArray(nums = [229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283]) == [228, 232, 231, 240, 249, 256, 259, 268, 263, 276, 280, 281]

Answer: assert Solution().minBitwiseArray(nums = [563, 569, 571, 577]) == [561, 568, 569, 576]

Answer: assert Solution().minBitwiseArray(nums = [607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709]) == [591, 612, 616, 617, 627, 640, 641, 643, 652, 657, 660, 672, 676, 681, 689, 700, 708]

Answer: assert Solution().minBitwiseArray(nums = [401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487]) == [400, 408, 417, 420, 423, 432, 435, 441, 448, 456, 460, 455, 465, 463, 483]

Answer: assert Solution().minBitwiseArray(nums = [1741, 1747, 1753, 1759]) == [1740, 1745, 1752, 1743]

Answer: assert Solution().minBitwiseArray(nums = [937, 941, 947, 953]) == [936, 940, 945, 952]

Answer: assert Solution().minBitwiseArray(nums = [307, 311, 313, 317]) == [305, 307, 312, 316]

Answer: assert Solution().minBitwiseArray(nums = [1483, 1487, 1489, 1493]) == [1481, 1479, 1488, 1492]

Answer: assert Solution().minBitwiseArray(nums = [3457, 3461, 3463, 3467]) == [3456, 3460, 3459, 3465]

Answer: assert Solution().minBitwiseArray(nums = [2389, 2393, 2399, 2411]) == [2388, 2392, 2383, 2409]

Answer: assert Solution().minBitwiseArray(nums = [587, 593, 599, 601]) == [585, 592, 595, 600]

Answer: assert Solution().minBitwiseArray(nums = [211, 223, 227, 229, 233, 239, 241, 251, 257, 263]) == [209, 207, 225, 228, 232, 231, 240, 249, 256, 259]

Answer: assert Solution().minBitwiseArray(nums = [1709, 1721, 1723, 1733]) == [1708, 1720, 1721, 1732]

Answer: assert Solution().minBitwiseArray(nums = [653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797]) == [652, 657, 660, 672, 676, 681, 689, 700, 708, 711, 723, 732, 737, 739, 743, 756, 760, 768, 772, 785, 796]

Answer: assert Solution().minBitwiseArray(nums = [677, 683, 691, 701]) == [676, 681, 689, 700]

Answer: assert Solution().minBitwiseArray(nums = [809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997]) == [808, 809, 820, 819, 825, 828, 835, 852, 856, 857, 847, 876, 880, 881, 883, 905, 903, 915, 928, 936, 940, 945, 952, 963, 969, 976, 979, 975, 996]

Answer: assert Solution().minBitwiseArray(nums = [3793, 3797, 3803, 3821]) == [3792, 3796, 3801, 3820]

Answer: assert Solution().minBitwiseArray(nums = [467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577]) == [465, 463, 483, 489, 497, 499, 508, 520, 521, 540, 545, 556, 561, 568, 569, 576]

Answer: assert Solution().minBitwiseArray(nums = [2857, 2861, 2879, 2887]) == [2856, 2860, 2847, 2883]

Answer: assert Solution().minBitwiseArray(nums = [709, 719, 727, 733]) == [708, 711, 723, 732]

Answer: assert Solution().minBitwiseArray(nums = [2731, 2741, 2749, 2753]) == [2729, 2740, 2748, 2752]

Answer: assert Solution().minBitwiseArray(nums = [1777, 1783, 1787, 1789]) == [1776, 1779, 1785, 1788]

Answer: assert Solution().minBitwiseArray(nums = [353, 373, 389, 401, 419, 431, 443]) == [352, 372, 388, 400, 417, 423, 441]

Answer: assert Solution().minBitwiseArray(nums = [1453, 1459, 1471, 1481]) == [1452, 1457, 1439, 1480]

Answer: assert Solution().minBitwiseArray(nums = [1039, 1049, 1051, 1061]) == [1031, 1048, 1049, 1060]

Answer: assert Solution().minBitwiseArray(nums = [151, 157, 163, 167, 173, 179, 181]) == [147, 156, 161, 163, 172, 177, 180]

Answer: assert Solution().minBitwiseArray(nums = [797, 809, 811, 821]) == [796, 808, 809, 820]

Answer: assert Solution().minBitwiseArray(nums = [313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379]) == [312, 316, 329, 336, 345, 348, 352, 355, 359, 372, 377]

Answer: assert Solution().minBitwiseArray(nums = [59, 61, 67, 71, 73, 79]) == [57, 60, 65, 67, 72, 71]

Answer: assert Solution().minBitwiseArray(nums = [1597, 1601, 1607, 1609]) == [1596, 1600, 1603, 1608]

Answer: assert Solution().minBitwiseArray(nums = [2767, 2777, 2789, 2791]) == [2759, 2776, 2788, 2787]

Answer: assert Solution().minBitwiseArray(nums = [461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563]) == [460, 455, 465, 463, 483, 489, 497, 499, 508, 520, 521, 540, 545, 556, 561]

Answer: assert Solution().minBitwiseArray(nums = [353, 359, 367, 373]) == [352, 355, 359, 372]

Answer: assert Solution().minBitwiseArray(nums = [1499, 1511, 1523, 1531]) == [1497, 1507, 1521, 1529]

Answer: assert Solution().minBitwiseArray(nums = [211, 223, 227, 229]) == [209, 207, 225, 228]

Answer: assert Solution().minBitwiseArray(nums = [149, 151, 157, 163]) == [148, 147, 156, 161]

Answer: assert Solution().minBitwiseArray(nums = [3343, 3347, 3359, 3361]) == [3335, 3345, 3343, 3360]

Answer: assert Solution().minBitwiseArray(nums = [1567, 1571, 1579, 1583]) == [1551, 1569, 1577, 1575]

Answer: assert Solution().minBitwiseArray(nums = [3217, 3221, 3229, 3251]) == [3216, 3220, 3228, 3249]

Answer: assert Solution().minBitwiseArray(nums = [653, 659, 661, 673]) == [652, 657, 660, 672]

Answer: assert Solution().minBitwiseArray(nums = [191, 193, 197, 199, 211, 223, 227, 229]) == [159, 192, 196, 195, 209, 207, 225, 228]

Answer: assert Solution().minBitwiseArray(nums = [2281, 2287, 2293, 2297]) == [2280, 2279, 2292, 2296]

Answer: assert Solution().minBitwiseArray(nums = [199, 211, 223, 227, 229, 233, 239, 241, 251]) == [195, 209, 207, 225, 228, 232, 231, 240, 249]

Answer: assert Solution().minBitwiseArray(nums = [463, 487, 503, 521, 541, 563, 571]) == [455, 483, 499, 520, 540, 561, 569]

Answer: assert Solution().minBitwiseArray(nums = [3559, 3571, 3581, 3583]) == [3555, 3569, 3580, 3327]

Answer: assert Solution().minBitwiseArray(nums = [233, 239, 241, 251]) == [232, 231, 240, 249]

Answer: assert Solution().minBitwiseArray(nums = [2341, 2347, 2351, 2357]) == [2340, 2345, 2343, 2356]

Answer: assert Solution().minBitwiseArray(nums = [2113, 2129, 2131, 2137]) == [2112, 2128, 2129, 2136]

Answer: assert Solution().minBitwiseArray(nums = [2671, 2677, 2683, 2687]) == [2663, 2676, 2681, 2623]

Answer: assert Solution().minBitwiseArray(nums = [3539, 3541, 3547, 3557]) == [3537, 3540, 3545, 3556]

Answer: assert Solution().minBitwiseArray(nums = [283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353]) == [281, 292, 305, 307, 312, 316, 329, 336, 345, 348, 352]

Answer: assert Solution().minBitwiseArray(nums = [113, 127, 131, 137, 139, 149, 151]) == [112, 63, 129, 136, 137, 148, 147]

Answer: assert Solution().minBitwiseArray(nums = [853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997]) == [852, 856, 857, 847, 876, 880, 881, 883, 905, 903, 915, 928, 936, 940, 945, 952, 963, 969, 976, 979, 975, 996]

Answer: assert Solution().minBitwiseArray(nums = [991, 997, 1009, 1013]) == [975, 996, 1008, 1012]

Answer: assert Solution().minBitwiseArray(nums = [1543, 1549, 1553, 1559]) == [1539, 1548, 1552, 1555]

Answer: assert Solution().minBitwiseArray(nums = [3469, 3491, 3499, 3511]) == [3468, 3489, 3497, 3507]

Answer: assert Solution().minBitwiseArray(nums = [823, 827, 829, 839]) == [819, 825, 828, 835]

Answer: assert Solution().minBitwiseArray(nums = [2557, 2579, 2591, 2593]) == [2556, 2577, 2575, 2592]

Answer: assert Solution().minBitwiseArray(nums = [1999, 2003, 2011, 2017]) == [1991, 2001, 2009, 2016]

Answer: assert Solution().minBitwiseArray(nums = [2833, 2837, 2843, 2851]) == [2832, 2836, 2841, 2849]

Answer: assert Solution().minBitwiseArray(nums = [211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269]) == [209, 207, 225, 228, 232, 231, 240, 249, 256, 259, 268]

Answer: assert Solution().minBitwiseArray(nums = [587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677]) == [585, 592, 595, 600, 591, 612, 616, 617, 627, 640, 641, 643, 652, 657, 660, 672, 676]

Answer: assert Solution().minBitwiseArray(nums = [167, 173, 179, 181]) == [163, 172, 177, 180]

Answer: assert Solution().minBitwiseArray(nums = [2221, 2237, 2239, 2243]) == [2220, 2236, 2207, 2241]

Answer: assert Solution().minBitwiseArray(nums = [83, 89, 97, 101, 103, 107, 109, 113]) == [81, 88, 96, 100, 99, 105, 108, 112]

Answer: assert Solution().minBitwiseArray(nums = [103, 131, 151, 173, 197, 211]) == [99, 129, 147, 172, 196, 209]

Answer: assert Solution().minBitwiseArray(nums = [2251, 2267, 2269, 2273]) == [2249, 2265, 2268, 2272]

Answer: assert Solution().minBitwiseArray(nums = [1093, 1097, 1103, 1109]) == [1092, 1096, 1095, 1108]

Answer: assert Solution().minBitwiseArray(nums = [3001, 3011, 3019, 3023]) == [3000, 3009, 3017, 3015]

Answer: assert Solution().minBitwiseArray(nums = [2539, 2543, 2549, 2551]) == [2537, 2535, 2548, 2547]

Answer: assert Solution().minBitwiseArray(nums = [1801, 1811, 1823, 1831]) == [1800, 1809, 1807, 1827]

Answer: assert Solution().minBitwiseArray(nums = [83, 97, 101, 103, 107]) == [81, 96, 100, 99, 105]

Answer: assert Solution().minBitwiseArray(nums = [593, 601, 613, 617, 631, 641, 643, 653]) == [592, 600, 612, 616, 627, 640, 641, 652]

Answer: assert Solution().minBitwiseArray(nums = [83, 89, 97, 101, 103, 107]) == [81, 88, 96, 100, 99, 105]

Answer: assert Solution().minBitwiseArray(nums = [1063, 1069, 1087, 1091]) == [1059, 1068, 1055, 1089]

Answer: assert Solution().minBitwiseArray(nums = [751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823]) == [743, 756, 760, 768, 772, 785, 796, 808, 809, 820, 819]

Answer: assert Solution().minBitwiseArray(nums = [2609, 2617, 2621, 2633]) == [2608, 2616, 2620, 2632]

Answer: assert Solution().minBitwiseArray(nums = [113, 127, 131, 137, 139, 149, 151, 157]) == [112, 63, 129, 136, 137, 148, 147, 156]

Answer: assert Solution().minBitwiseArray(nums = [1637, 1657, 1663, 1667]) == [1636, 1656, 1599, 1665]

Answer: assert Solution().minBitwiseArray(nums = [727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997]) == [723, 732, 737, 739, 743, 756, 760, 768, 772, 785, 796, 808, 809, 820, 819, 825, 828, 835, 852, 856, 857, 847, 876, 880, 881, 883, 905, 903, 915, 928, 936, 940, 945, 952, 963, 969, 976, 979, 975, 996]

Answer: assert Solution().minBitwiseArray(nums = [1433, 1439, 1447, 1451]) == [1432, 1423, 1443, 1449]

Answer: assert Solution().minBitwiseArray(nums = [631, 641, 643, 647]) == [627, 640, 641, 643]

Answer: assert Solution().minBitwiseArray(nums = [1669, 1693, 1697, 1699]) == [1668, 1692, 1696, 1697]

Answer: assert Solution().minBitwiseArray(nums = [179, 181, 191, 193, 197, 199, 211, 223, 227]) == [177, 180, 159, 192, 196, 195, 209, 207, 225]

Answer: assert Solution().minBitwiseArray(nums = [83, 89, 97, 101, 103]) == [81, 88, 96, 100, 99]

Answer: assert Solution().minBitwiseArray(nums = [59, 61, 67, 71, 73]) == [57, 60, 65, 67, 72]

Answer: assert Solution().minBitwiseArray(nums = [89, 97, 101, 103]) == [88, 96, 100, 99]

Answer: assert Solution().minBitwiseArray(nums = [409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487]) == [408, 417, 420, 423, 432, 435, 441, 448, 456, 460, 455, 465, 463, 483]

Answer: assert Solution().minBitwiseArray(nums = [127, 131, 137, 139, 149, 151, 157]) == [63, 129, 136, 137, 148, 147, 156]

Answer: assert Solution().minBitwiseArray(nums = [139, 149, 151, 157, 163, 167, 173]) == [137, 148, 147, 156, 161, 163, 172]

Answer: assert Solution().minBitwiseArray(nums = [2897, 2903, 2909, 2917]) == [2896, 2899, 2908, 2916]

Answer: assert Solution().minBitwiseArray(nums = [401, 409, 419, 421]) == [400, 408, 417, 420]

Answer: assert Solution().minBitwiseArray(nums = [127, 131, 137, 139, 149, 151, 157, 163, 167]) == [63, 129, 136, 137, 148, 147, 156, 161, 163]

Answer: assert Solution().minBitwiseArray(nums = [1217, 1223, 1229, 1231]) == [1216, 1219, 1228, 1223]

Answer: assert Solution().minBitwiseArray(nums = [367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499]) == [359, 372, 377, 319, 388, 396, 400, 408, 417, 420, 423, 432, 435, 441, 448, 456, 460, 455, 465, 463, 483, 489, 497]

Answer: assert Solution().minBitwiseArray(nums = [263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317]) == [259, 268, 263, 276, 280, 281, 292, 305, 307, 312, 316]

Answer: assert Solution().minBitwiseArray(nums = [1873, 1877, 1879, 1889]) == [1872, 1876, 1875, 1888]

Answer: assert Solution().minBitwiseArray(nums = [2477, 2503, 2521, 2531]) == [2476, 2499, 2520, 2529]

Answer: assert Solution().minBitwiseArray(nums = [383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457]) == [319, 388, 396, 400, 408, 417, 420, 423, 432, 435, 441, 448, 456]

Answer: assert Solution().minBitwiseArray(nums = [113, 127, 131, 137, 139, 149]) == [112, 63, 129, 136, 137, 148]

Answer: assert Solution().minBitwiseArray(nums = [443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541]) == [441, 448, 456, 460, 455, 465, 463, 483, 489, 497, 499, 508, 520, 521, 540]

Answer: assert Solution().minBitwiseArray(nums = [257, 263, 269, 271, 277, 281, 283, 293, 307, 311]) == [256, 259, 268, 263, 276, 280, 281, 292, 305, 307]

Answer: assert Solution().minBitwiseArray(nums = [331, 337, 347, 349]) == [329, 336, 345, 348]

Answer: assert Solution().minBitwiseArray(nums = [911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997]) == [903, 915, 928, 936, 940, 945, 952, 963, 969, 976, 979, 975, 996]

Answer: assert Solution().minBitwiseArray(nums = [233, 251, 271, 281, 311, 331]) == [232, 249, 263, 280, 307, 329]

Answer: assert Solution().minBitwiseArray(nums = [1979, 1987, 1993, 1997]) == [1977, 1985, 1992, 1996]

Answer: assert Solution().minBitwiseArray(nums = [257, 263, 269, 271]) == [256, 259, 268, 263]

Answer: assert Solution().minBitwiseArray(nums = [2371, 2377, 2381, 2383]) == [2369, 2376, 2380, 2375]

Answer: assert Solution().minBitwiseArray(nums = [3253, 3257, 3259, 3271]) == [3252, 3256, 3257, 3267]

Answer: assert Solution().minBitwiseArray(nums = [2027, 2029, 2039, 2053]) == [2025, 2028, 2035, 2052]

Answer: assert Solution().minBitwiseArray(nums = [3517, 3527, 3529, 3533]) == [3516, 3523, 3528, 3532]

Answer: assert Solution().minBitwiseArray(nums = [2447, 2459, 2467, 2473]) == [2439, 2457, 2465, 2472]

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 minBitwiseArray(self, nums: List[int]) -> List[int]:
        ans = []
        for x in nums:
            if x == 2:
                ans.append(-1)
            else:
                for i in range(1, 32):
                    if x >> i & 1 ^ 1:
                        ans.append(x ^ 1 << (i - 1))
                        break
        return ans