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 a string s and an integer k, return the total number of substrings of s where at least one character appears at least k times.

Example 1:

Input: s = "abacb", k = 2
Output: 4
Explanation:
The valid substrings are:

"aba" (character 'a' appears 2 times).
"abac" (character 'a' appears 2 times).
"abacb" (character 'a' appears 2 times).
"bacb" (character 'b' appears 2 times).

Example 2:

Input: s = "abcde", k = 1
Output: 15
Explanation:
All substrings are valid because every character appears at least once.

Constraints:

1 <= s.length <= 3000
1 <= k <= s.length
s consists only of lowercase English letters.

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

SOLUTION:

Question:
PROBLEM:
Given a string s and an integer k, return the total number of substrings of s where at least one character appears at least k times.

Example 1:

Input: s = "abacb", k = 2
Output: 4
Explanation:
The valid substrings are:

"aba" (character 'a' appears 2 times).
"abac" (character 'a' appears 2 times).
"abacb" (character 'a' appears 2 times).
"bacb" (character 'b' appears 2 times).

Example 2:

Input: s = "abcde", k = 1
Output: 15
Explanation:
All substrings are valid because every character appears at least once.

Constraints:

1 <= s.length <= 3000
1 <= k <= s.length
s consists only of lowercase English letters.

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

SOLUTION:

assert Solution().numberOfSubstrings(s = "pqr", k = 1) == 6

assert Solution().numberOfSubstrings(s = "aabbccc", k = 3) == 5

assert Solution().numberOfSubstrings(s = "aaabb", k = 3) == 3

assert Solution().numberOfSubstrings(s = "zzzzzz", k = 4) == 6

assert Solution().numberOfSubstrings(s = "abcde", k = 1) == 15

assert Solution().numberOfSubstrings(s = "abcdabc", k = 2) == 6

assert Solution().numberOfSubstrings(s = "abcdabcd", k = 1) == 36

assert Solution().numberOfSubstrings(s = "xyz", k = 1) == 6

assert Solution().numberOfSubstrings(s = "abcdefg", k = 2) == 0

assert Solution().numberOfSubstrings(s = "zzzz", k = 2) == 6

assert Solution().numberOfSubstrings(s = "aaaa", k = 2) == 6

assert Solution().numberOfSubstrings(s = "a", k = 1) == 1

assert Solution().numberOfSubstrings(s = "xyzxyz", k = 2) == 6

assert Solution().numberOfSubstrings(s = "abacb", k = 2) == 4

assert Solution().numberOfSubstrings(s = "pqrqpq", k = 2) == 8

assert Solution().numberOfSubstrings(s = "zzzzzzzz", k = 4) == 15

assert Solution().numberOfSubstrings(s = "aaaaa", k = 3) == 6

assert Solution().numberOfSubstrings(s = "xyzxyzxyz", k = 3) == 6

assert Solution().numberOfSubstrings(s = "aabbcc", k = 2) == 13

assert Solution().numberOfSubstrings(s = "ababab", k = 3) == 3

assert Solution().numberOfSubstrings(s = "abacbacbacb", k = 2) == 37

assert Solution().numberOfSubstrings(s = "aaaabbbbcccc", k = 3) == 49

assert Solution().numberOfSubstrings(s = "aaaabbbbccccddddeeeeffff", k = 4) == 201

assert Solution().numberOfSubstrings(s = "aaabbbcccdddfffggghhhiiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz", k = 4) == 1144

assert Solution().numberOfSubstrings(s = "abacbacbacb", k = 3) == 16

assert Solution().numberOfSubstrings(s = "abcdabcdabcdabcd", k = 4) == 10

assert Solution().numberOfSubstrings(s = "abcdefabcdefabcdef", k = 3) == 21

assert Solution().numberOfSubstrings(s = "aaaaabbbbbcccccdddddeeeeeffffffggggg", k = 4) == 525

assert Solution().numberOfSubstrings(s = "aabbaabbaabbaabbccddccddccddeeffeegghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", k = 2) == 2665

assert Solution().numberOfSubstrings(s = "zzzzzzzzzzz", k = 5) == 28

assert Solution().numberOfSubstrings(s = "banana", k = 2) == 9

assert Solution().numberOfSubstrings(s = "zzzzzzzzzz", k = 3) == 36

assert Solution().numberOfSubstrings(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", k = 10) == 1431

assert Solution().numberOfSubstrings(s = "zzzzzzzzzzzzzzzzzzzz", k = 5) == 136

assert Solution().numberOfSubstrings(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", k = 1) == 1378

assert Solution().numberOfSubstrings(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", k = 10) == 4753

assert Solution().numberOfSubstrings(s = "aabacbebebebebebebebebebebebebebebebebebebebebebebebe", k = 3) == 1220

assert Solution().numberOfSubstrings(s = "thisisaverylongstringthatweneedtocheck", k = 2) == 542

assert Solution().numberOfSubstrings(s = "ababababababababababababababababababababababababababababababab", k = 3) == 1711

assert Solution().numberOfSubstrings(s = "aaaabbbbccccddddeeeeffffgggghhhhiiiijjjjkkkkllll", k = 4) == 969

assert Solution().numberOfSubstrings(s = "abcdefabcdefabcdefabcdef", k = 2) == 171

assert Solution().numberOfSubstrings(s = "qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq", k = 5) == 1275

assert Solution().numberOfSubstrings(s = "abcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabc", k = 5) == 1326

assert Solution().numberOfSubstrings(s = "mississippi", k = 2) == 46

assert Solution().numberOfSubstrings(s = "aaaaaaaaaabbbbbbbbccccccccdddddddd", k = 5) == 435

assert Solution().numberOfSubstrings(s = "abcdabcdabcdabcdabcdabcdabcdabcdabcdabcd", k = 3) == 528

assert Solution().numberOfSubstrings(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", k = 15) == 741

assert Solution().numberOfSubstrings(s = "abcdefabcdefabcdef", k = 2) == 78

assert Solution().numberOfSubstrings(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", k = 25) == 55

assert Solution().numberOfSubstrings(s = "mnopqrspqrstuvspqrstuvwspqrstuvwxspqrstuvwxy", k = 3) == 549

assert Solution().numberOfSubstrings(s = "mmmmnnnnooooppppqqqqrrrrssssttttuuuuvvvvwwwwxxxxyyyyzzzz", k = 4) == 1353

assert Solution().numberOfSubstrings(s = "ababababab", k = 2) == 36

assert Solution().numberOfSubstrings(s = "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa", k = 10) == 861

assert Solution().numberOfSubstrings(s = "thisisaverylongstringwithseveralcharacters", k = 2) == 669

assert Solution().numberOfSubstrings(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", k = 26) == 0

assert Solution().numberOfSubstrings(s = "abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz", k = 2) == 351

assert Solution().numberOfSubstrings(s = "xyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyz", k = 3) == 1830

assert Solution().numberOfSubstrings(s = "ababcbacadefegdehijhklij", k = 2) == 219

assert Solution().numberOfSubstrings(s = "abcdefgabcdefgabcdefgabcdefgabcdefgabcdefgabcdefg", k = 2) == 903

assert Solution().numberOfSubstrings(s = "abcabcabc", k = 3) == 6

assert Solution().numberOfSubstrings(s = "abcdefabcdefabcdefabcdefabcdefabcdefabcdefabcdefabcdef", k = 2) == 1176

assert Solution().numberOfSubstrings(s = "thefastbrownfoxjumpsoverthelazydog", k = 1) == 595

assert Solution().numberOfSubstrings(s = "ababababababababababababababababa", k = 2) == 496

assert Solution().numberOfSubstrings(s = "banana", k = 3) == 2

assert Solution().numberOfSubstrings(s = "xyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxy", k = 3) == 528

assert Solution().numberOfSubstrings(s = "abcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcd", k = 5) == 990

assert Solution().numberOfSubstrings(s = "xzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzy", k = 5) == 561

assert Solution().numberOfSubstrings(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzxyzabc", k = 2) == 1611

assert Solution().numberOfSubstrings(s = "abcdefghijklmnopqrstuvxyzabcdefghijklmnopqrstuvxyz", k = 2) == 325

assert Solution().numberOfSubstrings(s = "abcabcabcabcabcabcabcabcabcabc", k = 3) == 300

assert Solution().numberOfSubstrings(s = "loremipsumloremipsumloremipsum", k = 2) == 275

assert Solution().numberOfSubstrings(s = "abcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabc", k = 10) == 561

assert Solution().numberOfSubstrings(s = "abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz", k = 3) == 351

assert Solution().numberOfSubstrings(s = "thisisaverylongstringwithvariouscharactersandfrequencies", k = 3) == 919

assert Solution().numberOfSubstrings(s = "ababababababababababababababababababababababababa", k = 2) == 1128

assert Solution().numberOfSubstrings(s = "abcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabc", k = 15) == 231

assert Solution().numberOfSubstrings(s = "abcdefg", k = 1) == 28

assert Solution().numberOfSubstrings(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", k = 10) == 3655

assert Solution().numberOfSubstrings(s = "abcdeabcdeabcde", k = 3) == 15

assert Solution().numberOfSubstrings(s = "abcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabc", k = 4) == 2016

assert Solution().numberOfSubstrings(s = "aabbaabbaabbcccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", k = 2) == 1801

assert Solution().numberOfSubstrings(s = "xyzzzzxyzzzzxyzzzz", k = 4) == 99

assert Solution().numberOfSubstrings(s = "abcdefghijklmnopqrstuvwxyz", k = 1) == 351

assert Solution().numberOfSubstrings(s = "abacabadabacaba", k = 3) == 61

assert Solution().numberOfSubstrings(s = "abcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabc", k = 5) == 903

assert Solution().numberOfSubstrings(s = "aaaaaaaaaabbbbbbbbbbccccccccccdddddddddd", k = 5) == 636

assert Solution().numberOfSubstrings(s = "xxyyzzxxyyzzxxyyzz", k = 3) == 78

assert Solution().numberOfSubstrings(s = "xyxyxyxyxyxyxyxy", k = 4) == 55

assert Solution().numberOfSubstrings(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", k = 3) == 0

assert Solution().numberOfSubstrings(s = "ababababababababababababababababababababababababababab", k = 4) == 1176

assert Solution().numberOfSubstrings(s = "xxyyzzxxyyzzxxyyzzxxyyzzxxyyzzxxyyzzxxyyzz", k = 4) == 613

assert Solution().numberOfSubstrings(s = "abcdefabcdefabcdefabcdefabcdef", k = 1) == 465

assert Solution().numberOfSubstrings(s = "aaaaaaaaabbbbbbbbb", k = 5) == 95

assert Solution().numberOfSubstrings(s = "aaaaaaaaaabbbbbbbbbbcccccccccc", k = 3) == 400

assert Solution().numberOfSubstrings(s = "mnopqrstuvmnopqrstuvmnopqrstuvmnopqrstuvmnopqrstuvmnopqrstuvmnopqrstuvmnopqrstuv", k = 3) == 1830

assert Solution().numberOfSubstrings(s = "aabacbbcc", k = 2) == 29

assert Solution().numberOfSubstrings(s = "abababababababab", k = 2) == 105

assert Solution().numberOfSubstrings(s = "amazingracecar", k = 2) == 45

assert Solution().numberOfSubstrings(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", k = 2) == 1301

assert Solution().numberOfSubstrings(s = "aabbbcccdddeee", k = 3) == 66

assert Solution().numberOfSubstrings(s = "zzzzzzzzz", k = 5) == 15

assert Solution().numberOfSubstrings(s = "xyzyxyzyxyzyxyzy", k = 2) == 98

Answer: assert Solution().numberOfSubstrings(s = "pqr", k = 1) == 6

Answer: assert Solution().numberOfSubstrings(s = "aabbccc", k = 3) == 5

Answer: assert Solution().numberOfSubstrings(s = "aaabb", k = 3) == 3

Answer: assert Solution().numberOfSubstrings(s = "zzzzzz", k = 4) == 6

Answer: assert Solution().numberOfSubstrings(s = "abcde", k = 1) == 15

Answer: assert Solution().numberOfSubstrings(s = "abcdabc", k = 2) == 6

Answer: assert Solution().numberOfSubstrings(s = "abcdabcd", k = 1) == 36

Answer: assert Solution().numberOfSubstrings(s = "xyz", k = 1) == 6

Answer: assert Solution().numberOfSubstrings(s = "abcdefg", k = 2) == 0

Answer: assert Solution().numberOfSubstrings(s = "zzzz", k = 2) == 6

Answer: assert Solution().numberOfSubstrings(s = "aaaa", k = 2) == 6

Answer: assert Solution().numberOfSubstrings(s = "a", k = 1) == 1

Answer: assert Solution().numberOfSubstrings(s = "xyzxyz", k = 2) == 6

Answer: assert Solution().numberOfSubstrings(s = "abacb", k = 2) == 4

Answer: assert Solution().numberOfSubstrings(s = "pqrqpq", k = 2) == 8

Answer: assert Solution().numberOfSubstrings(s = "zzzzzzzz", k = 4) == 15

Answer: assert Solution().numberOfSubstrings(s = "aaaaa", k = 3) == 6

Answer: assert Solution().numberOfSubstrings(s = "xyzxyzxyz", k = 3) == 6

Answer: assert Solution().numberOfSubstrings(s = "aabbcc", k = 2) == 13

Answer: assert Solution().numberOfSubstrings(s = "ababab", k = 3) == 3

Answer: assert Solution().numberOfSubstrings(s = "abacbacbacb", k = 2) == 37

Answer: assert Solution().numberOfSubstrings(s = "aaaabbbbcccc", k = 3) == 49

Answer: assert Solution().numberOfSubstrings(s = "aaaabbbbccccddddeeeeffff", k = 4) == 201

Answer: assert Solution().numberOfSubstrings(s = "aaabbbcccdddfffggghhhiiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz", k = 4) == 1144

Answer: assert Solution().numberOfSubstrings(s = "abacbacbacb", k = 3) == 16

Answer: assert Solution().numberOfSubstrings(s = "abcdabcdabcdabcd", k = 4) == 10

Answer: assert Solution().numberOfSubstrings(s = "abcdefabcdefabcdef", k = 3) == 21

Answer: assert Solution().numberOfSubstrings(s = "aaaaabbbbbcccccdddddeeeeeffffffggggg", k = 4) == 525

Answer: assert Solution().numberOfSubstrings(s = "aabbaabbaabbaabbccddccddccddeeffeegghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", k = 2) == 2665

Answer: assert Solution().numberOfSubstrings(s = "zzzzzzzzzzz", k = 5) == 28

Answer: assert Solution().numberOfSubstrings(s = "banana", k = 2) == 9

Answer: assert Solution().numberOfSubstrings(s = "zzzzzzzzzz", k = 3) == 36

Answer: assert Solution().numberOfSubstrings(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", k = 10) == 1431

Answer: assert Solution().numberOfSubstrings(s = "zzzzzzzzzzzzzzzzzzzz", k = 5) == 136

Answer: assert Solution().numberOfSubstrings(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", k = 1) == 1378

Answer: assert Solution().numberOfSubstrings(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", k = 10) == 4753

Answer: assert Solution().numberOfSubstrings(s = "aabacbebebebebebebebebebebebebebebebebebebebebebebebe", k = 3) == 1220

Answer: assert Solution().numberOfSubstrings(s = "thisisaverylongstringthatweneedtocheck", k = 2) == 542

Answer: assert Solution().numberOfSubstrings(s = "ababababababababababababababababababababababababababababababab", k = 3) == 1711

Answer: assert Solution().numberOfSubstrings(s = "aaaabbbbccccddddeeeeffffgggghhhhiiiijjjjkkkkllll", k = 4) == 969

Answer: assert Solution().numberOfSubstrings(s = "abcdefabcdefabcdefabcdef", k = 2) == 171

Answer: assert Solution().numberOfSubstrings(s = "qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq", k = 5) == 1275

Answer: assert Solution().numberOfSubstrings(s = "abcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabc", k = 5) == 1326

Answer: assert Solution().numberOfSubstrings(s = "mississippi", k = 2) == 46

Answer: assert Solution().numberOfSubstrings(s = "aaaaaaaaaabbbbbbbbccccccccdddddddd", k = 5) == 435

Answer: assert Solution().numberOfSubstrings(s = "abcdabcdabcdabcdabcdabcdabcdabcdabcdabcd", k = 3) == 528

Answer: assert Solution().numberOfSubstrings(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", k = 15) == 741

Answer: assert Solution().numberOfSubstrings(s = "abcdefabcdefabcdef", k = 2) == 78

Answer: assert Solution().numberOfSubstrings(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", k = 25) == 55

Answer: assert Solution().numberOfSubstrings(s = "mnopqrspqrstuvspqrstuvwspqrstuvwxspqrstuvwxy", k = 3) == 549

Answer: assert Solution().numberOfSubstrings(s = "mmmmnnnnooooppppqqqqrrrrssssttttuuuuvvvvwwwwxxxxyyyyzzzz", k = 4) == 1353

Answer: assert Solution().numberOfSubstrings(s = "ababababab", k = 2) == 36

Answer: assert Solution().numberOfSubstrings(s = "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa", k = 10) == 861

Answer: assert Solution().numberOfSubstrings(s = "thisisaverylongstringwithseveralcharacters", k = 2) == 669

Answer: assert Solution().numberOfSubstrings(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", k = 26) == 0

Answer: assert Solution().numberOfSubstrings(s = "abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz", k = 2) == 351

Answer: assert Solution().numberOfSubstrings(s = "xyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyz", k = 3) == 1830

Answer: assert Solution().numberOfSubstrings(s = "ababcbacadefegdehijhklij", k = 2) == 219

Answer: assert Solution().numberOfSubstrings(s = "abcdefgabcdefgabcdefgabcdefgabcdefgabcdefgabcdefg", k = 2) == 903

Answer: assert Solution().numberOfSubstrings(s = "abcabcabc", k = 3) == 6

Answer: assert Solution().numberOfSubstrings(s = "abcdefabcdefabcdefabcdefabcdefabcdefabcdefabcdefabcdef", k = 2) == 1176

Answer: assert Solution().numberOfSubstrings(s = "thefastbrownfoxjumpsoverthelazydog", k = 1) == 595

Answer: assert Solution().numberOfSubstrings(s = "ababababababababababababababababa", k = 2) == 496

Answer: assert Solution().numberOfSubstrings(s = "banana", k = 3) == 2

Answer: assert Solution().numberOfSubstrings(s = "xyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxy", k = 3) == 528

Answer: assert Solution().numberOfSubstrings(s = "abcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcd", k = 5) == 990

Answer: assert Solution().numberOfSubstrings(s = "xzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzy", k = 5) == 561

Answer: assert Solution().numberOfSubstrings(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzxyzabc", k = 2) == 1611

Answer: assert Solution().numberOfSubstrings(s = "abcdefghijklmnopqrstuvxyzabcdefghijklmnopqrstuvxyz", k = 2) == 325

Answer: assert Solution().numberOfSubstrings(s = "abcabcabcabcabcabcabcabcabcabc", k = 3) == 300

Answer: assert Solution().numberOfSubstrings(s = "loremipsumloremipsumloremipsum", k = 2) == 275

Answer: assert Solution().numberOfSubstrings(s = "abcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabc", k = 10) == 561

Answer: assert Solution().numberOfSubstrings(s = "abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz", k = 3) == 351

Answer: assert Solution().numberOfSubstrings(s = "thisisaverylongstringwithvariouscharactersandfrequencies", k = 3) == 919

Answer: assert Solution().numberOfSubstrings(s = "ababababababababababababababababababababababababa", k = 2) == 1128

Answer: assert Solution().numberOfSubstrings(s = "abcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabc", k = 15) == 231

Answer: assert Solution().numberOfSubstrings(s = "abcdefg", k = 1) == 28

Answer: assert Solution().numberOfSubstrings(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", k = 10) == 3655

Answer: assert Solution().numberOfSubstrings(s = "abcdeabcdeabcde", k = 3) == 15

Answer: assert Solution().numberOfSubstrings(s = "abcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabc", k = 4) == 2016

Answer: assert Solution().numberOfSubstrings(s = "aabbaabbaabbcccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", k = 2) == 1801

Answer: assert Solution().numberOfSubstrings(s = "xyzzzzxyzzzzxyzzzz", k = 4) == 99

Answer: assert Solution().numberOfSubstrings(s = "abcdefghijklmnopqrstuvwxyz", k = 1) == 351

Answer: assert Solution().numberOfSubstrings(s = "abacabadabacaba", k = 3) == 61

Answer: assert Solution().numberOfSubstrings(s = "abcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabc", k = 5) == 903

Answer: assert Solution().numberOfSubstrings(s = "aaaaaaaaaabbbbbbbbbbccccccccccdddddddddd", k = 5) == 636

Answer: assert Solution().numberOfSubstrings(s = "xxyyzzxxyyzzxxyyzz", k = 3) == 78

Answer: assert Solution().numberOfSubstrings(s = "xyxyxyxyxyxyxyxy", k = 4) == 55

Answer: assert Solution().numberOfSubstrings(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", k = 3) == 0

Answer: assert Solution().numberOfSubstrings(s = "ababababababababababababababababababababababababababab", k = 4) == 1176

Answer: assert Solution().numberOfSubstrings(s = "xxyyzzxxyyzzxxyyzzxxyyzzxxyyzzxxyyzzxxyyzz", k = 4) == 613

Answer: assert Solution().numberOfSubstrings(s = "abcdefabcdefabcdefabcdefabcdef", k = 1) == 465

Answer: assert Solution().numberOfSubstrings(s = "aaaaaaaaabbbbbbbbb", k = 5) == 95

Answer: assert Solution().numberOfSubstrings(s = "aaaaaaaaaabbbbbbbbbbcccccccccc", k = 3) == 400

Answer: assert Solution().numberOfSubstrings(s = "mnopqrstuvmnopqrstuvmnopqrstuvmnopqrstuvmnopqrstuvmnopqrstuvmnopqrstuvmnopqrstuv", k = 3) == 1830

Answer: assert Solution().numberOfSubstrings(s = "aabacbbcc", k = 2) == 29

Answer: assert Solution().numberOfSubstrings(s = "abababababababab", k = 2) == 105

Answer: assert Solution().numberOfSubstrings(s = "amazingracecar", k = 2) == 45

Answer: assert Solution().numberOfSubstrings(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", k = 2) == 1301

Answer: assert Solution().numberOfSubstrings(s = "aabbbcccdddeee", k = 3) == 66

Answer: assert Solution().numberOfSubstrings(s = "zzzzzzzzz", k = 5) == 15

Answer: assert Solution().numberOfSubstrings(s = "xyzyxyzyxyzyxyzy", k = 2) == 98

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 numberOfSubstrings(self, s: str, k: int) -> int:
        cnt = Counter()
        ans = l = 0
        for c in s:
            cnt[c] += 1
            while cnt[c] >= k:
                cnt[s[l]] -= 1
                l += 1
            ans += l
        return ans

class Solution:
    def numberOfSubstrings(self, s: str, k: int) -> int:


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 a string s and an integer k, return the total number of substrings of s where at least one character appears at least k times.

Example 1:

Input: s = "abacb", k = 2
Output: 4
Explanation:
The valid substrings are:

"aba" (character 'a' appears 2 times).
"abac" (character 'a' appears 2 times).
"abacb" (character 'a' appears 2 times).
"bacb" (character 'b' appears 2 times).

Example 2:

Input: s = "abcde", k = 1
Output: 15
Explanation:
All substrings are valid because every character appears at least once.

Constraints:

1 <= s.length <= 3 * 105
1 <= k <= s.length
s consists only of lowercase English letters.

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

SOLUTION:

Question:
PROBLEM:
Given a string s and an integer k, return the total number of substrings of s where at least one character appears at least k times.

Example 1:

Input: s = "abacb", k = 2
Output: 4
Explanation:
The valid substrings are:

"aba" (character 'a' appears 2 times).
"abac" (character 'a' appears 2 times).
"abacb" (character 'a' appears 2 times).
"bacb" (character 'b' appears 2 times).

Example 2:

Input: s = "abcde", k = 1
Output: 15
Explanation:
All substrings are valid because every character appears at least once.

Constraints:

1 <= s.length <= 3 * 105
1 <= k <= s.length
s consists only of lowercase English letters.

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

SOLUTION:

assert Solution().numberOfSubstrings(s = "mississippi", k = 2) == 46

assert Solution().numberOfSubstrings(s = "zzzzzz", k = 4) == 6

assert Solution().numberOfSubstrings(s = "abcde", k = 1) == 15

assert Solution().numberOfSubstrings(s = "aabbcc", k = 2) == 13

assert Solution().numberOfSubstrings(s = "abcdabcd", k = 2) == 10

assert Solution().numberOfSubstrings(s = "aabbaa", k = 3) == 3

assert Solution().numberOfSubstrings(s = "abababab", k = 3) == 10

assert Solution().numberOfSubstrings(s = "banana", k = 2) == 9

assert Solution().numberOfSubstrings(s = "abcdabcd", k = 1) == 36

assert Solution().numberOfSubstrings(s = "abacabadabacaba", k = 2) == 85

assert Solution().numberOfSubstrings(s = "xyz", k = 1) == 6

assert Solution().numberOfSubstrings(s = "abcdefg", k = 2) == 0

assert Solution().numberOfSubstrings(s = "zzzz", k = 2) == 6

assert Solution().numberOfSubstrings(s = "zzzz", k = 3) == 3

assert Solution().numberOfSubstrings(s = "abcabcabc", k = 3) == 6

assert Solution().numberOfSubstrings(s = "abcdefg", k = 1) == 28

assert Solution().numberOfSubstrings(s = "a", k = 1) == 1

assert Solution().numberOfSubstrings(s = "abacb", k = 2) == 4

assert Solution().numberOfSubstrings(s = "aaabbbccc", k = 3) == 22

assert Solution().numberOfSubstrings(s = "aaabbb", k = 3) == 7

assert Solution().numberOfSubstrings(s = "abcabcabc", k = 2) == 21

assert Solution().numberOfSubstrings(s = "qwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnm", k = 2) == 351

assert Solution().numberOfSubstrings(s = "aabbcc", k = 3) == 0

assert Solution().numberOfSubstrings(s = "abacaba", k = 2) == 13

assert Solution().numberOfSubstrings(s = "abcabcabcabc", k = 3) == 21

assert Solution().numberOfSubstrings(s = "xyzzxyzzxyzz", k = 2) == 53

assert Solution().numberOfSubstrings(s = "qqwweerrttyyuuiiooppllaaasssddffgg", k = 2) == 546

assert Solution().numberOfSubstrings(s = "abcdefghijklmnopqrstuvwxyz", k = 1) == 351

assert Solution().numberOfSubstrings(s = "abacabadabacaba", k = 3) == 61

assert Solution().numberOfSubstrings(s = "aaaaabbbbccccdddd", k = 4) == 87

assert Solution().numberOfSubstrings(s = "aabbbcccc", k = 3) == 22

assert Solution().numberOfSubstrings(s = "zzzzzzzzzz", k = 5) == 21

assert Solution().numberOfSubstrings(s = "abcabcabcabcabcabcabc", k = 3) == 120

assert Solution().numberOfSubstrings(s = "abcdefghijk", k = 1) == 66

assert Solution().numberOfSubstrings(s = "aaaabbbbccccdddd", k = 4) == 73

assert Solution().numberOfSubstrings(s = "abcabcabcabcabcabc", k = 2) == 120

assert Solution().numberOfSubstrings(s = "aaaaaabbbbbcccccdddddeeeee", k = 5) == 213

assert Solution().numberOfSubstrings(s = "aabbccddeeffgg", k = 2) == 85

assert Solution().numberOfSubstrings(s = "pppppppppppppppppppp", k = 15) == 21

assert Solution().numberOfSubstrings(s = "xyxyxyxyxy", k = 2) == 36

assert Solution().numberOfSubstrings(s = "xxyyzzxxyyzzxxyyzz", k = 3) == 78

assert Solution().numberOfSubstrings(s = "abcabcabcabc", k = 4) == 6

assert Solution().numberOfSubstrings(s = "aabbccddeeffgghhiijjkk", k = 2) == 221

assert Solution().numberOfSubstrings(s = "zzzzzzzzzzzzzzzzzzzzzz", k = 10) == 91

assert Solution().numberOfSubstrings(s = "hellohellohello", k = 3) == 45

assert Solution().numberOfSubstrings(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", k = 3) == 0

assert Solution().numberOfSubstrings(s = "ababababab", k = 2) == 36

assert Solution().numberOfSubstrings(s = "abcdefghijklmnopqrstuvwyxz", k = 1) == 351

assert Solution().numberOfSubstrings(s = "pppppppppppppppppppppppppp", k = 15) == 78

assert Solution().numberOfSubstrings(s = "qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq", k = 10) == 561

assert Solution().numberOfSubstrings(s = "aabbaaabbbaaabbaa", k = 3) == 100

assert Solution().numberOfSubstrings(s = "abababababababababababababababababababab", k = 5) == 528

assert Solution().numberOfSubstrings(s = "abcdefgabcdefg", k = 2) == 28

assert Solution().numberOfSubstrings(s = "aabbbccc", k = 3) == 15

assert Solution().numberOfSubstrings(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", k = 15) == 1953

assert Solution().numberOfSubstrings(s = "ababcabcab", k = 3) == 12

assert Solution().numberOfSubstrings(s = "aabbaaccc", k = 2) == 33

assert Solution().numberOfSubstrings(s = "abcdefghij", k = 1) == 55

assert Solution().numberOfSubstrings(s = "aaabbbcccdddeeefffggghhhiii", k = 3) == 301

assert Solution().numberOfSubstrings(s = "aabccba", k = 2) == 15

assert Solution().numberOfSubstrings(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", k = 1) == 1378

assert Solution().numberOfSubstrings(s = "aaabbbccc", k = 2) == 34

assert Solution().numberOfSubstrings(s = "aabbbccc", k = 2) == 26

assert Solution().numberOfSubstrings(s = "abcdefghij", k = 2) == 0

assert Solution().numberOfSubstrings(s = "abacabadabacabadabacaba", k = 2) == 221

assert Solution().numberOfSubstrings(s = "abcdabcdabcdabcd", k = 1) == 136

assert Solution().numberOfSubstrings(s = "mississippiissippi", k = 3) == 93

assert Solution().numberOfSubstrings(s = "aabbccdd", k = 2) == 25

assert Solution().numberOfSubstrings(s = "mnopqrstuvmnopqrstuvmnopqrstuvmnopqrstuvmnopqrstuvmnopqrstuvm", k = 5) == 231

assert Solution().numberOfSubstrings(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", k = 20) == 1128

assert Solution().numberOfSubstrings(s = "aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz", k = 4) == 0

assert Solution().numberOfSubstrings(s = "abcdefghijklmnopqrstuvwxyz", k = 2) == 0

assert Solution().numberOfSubstrings(s = "aaabbbcccdddeeefffggghhhhiii", k = 3) == 327

assert Solution().numberOfSubstrings(s = "abcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabc", k = 5) == 1485

assert Solution().numberOfSubstrings(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", k = 2) == 1301

assert Solution().numberOfSubstrings(s = "aabbbcccddd", k = 3) == 36

assert Solution().numberOfSubstrings(s = "xyzxyzxyzxyz", k = 3) == 21

assert Solution().numberOfSubstrings(s = "banana", k = 3) == 2

assert Solution().numberOfSubstrings(s = "xyzzyxzyzyxzyzxzyzxzyz", k = 2) == 200

assert Solution().numberOfSubstrings(s = "abacabadaba", k = 2) == 41

Answer: assert Solution().numberOfSubstrings(s = "mississippi", k = 2) == 46

Answer: assert Solution().numberOfSubstrings(s = "zzzzzz", k = 4) == 6

Answer: assert Solution().numberOfSubstrings(s = "abcde", k = 1) == 15

Answer: assert Solution().numberOfSubstrings(s = "aabbcc", k = 2) == 13

Answer: assert Solution().numberOfSubstrings(s = "abcdabcd", k = 2) == 10

Answer: assert Solution().numberOfSubstrings(s = "aabbaa", k = 3) == 3

Answer: assert Solution().numberOfSubstrings(s = "abababab", k = 3) == 10

Answer: assert Solution().numberOfSubstrings(s = "banana", k = 2) == 9

Answer: assert Solution().numberOfSubstrings(s = "abcdabcd", k = 1) == 36

Answer: assert Solution().numberOfSubstrings(s = "abacabadabacaba", k = 2) == 85

Answer: assert Solution().numberOfSubstrings(s = "xyz", k = 1) == 6

Answer: assert Solution().numberOfSubstrings(s = "abcdefg", k = 2) == 0

Answer: assert Solution().numberOfSubstrings(s = "zzzz", k = 2) == 6

Answer: assert Solution().numberOfSubstrings(s = "zzzz", k = 3) == 3

Answer: assert Solution().numberOfSubstrings(s = "abcabcabc", k = 3) == 6

Answer: assert Solution().numberOfSubstrings(s = "abcdefg", k = 1) == 28

Answer: assert Solution().numberOfSubstrings(s = "a", k = 1) == 1

Answer: assert Solution().numberOfSubstrings(s = "abacb", k = 2) == 4

Answer: assert Solution().numberOfSubstrings(s = "aaabbbccc", k = 3) == 22

Answer: assert Solution().numberOfSubstrings(s = "aaabbb", k = 3) == 7

Answer: assert Solution().numberOfSubstrings(s = "abcabcabc", k = 2) == 21

Answer: assert Solution().numberOfSubstrings(s = "qwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnm", k = 2) == 351

Answer: assert Solution().numberOfSubstrings(s = "aabbcc", k = 3) == 0

Answer: assert Solution().numberOfSubstrings(s = "abacaba", k = 2) == 13

Answer: assert Solution().numberOfSubstrings(s = "abcabcabcabc", k = 3) == 21

Answer: assert Solution().numberOfSubstrings(s = "xyzzxyzzxyzz", k = 2) == 53

Answer: assert Solution().numberOfSubstrings(s = "qqwweerrttyyuuiiooppllaaasssddffgg", k = 2) == 546

Answer: assert Solution().numberOfSubstrings(s = "abcdefghijklmnopqrstuvwxyz", k = 1) == 351

Answer: assert Solution().numberOfSubstrings(s = "abacabadabacaba", k = 3) == 61

Answer: assert Solution().numberOfSubstrings(s = "aaaaabbbbccccdddd", k = 4) == 87

Answer: assert Solution().numberOfSubstrings(s = "aabbbcccc", k = 3) == 22

Answer: assert Solution().numberOfSubstrings(s = "zzzzzzzzzz", k = 5) == 21

Answer: assert Solution().numberOfSubstrings(s = "abcabcabcabcabcabcabc", k = 3) == 120

Answer: assert Solution().numberOfSubstrings(s = "abcdefghijk", k = 1) == 66

Answer: assert Solution().numberOfSubstrings(s = "aaaabbbbccccdddd", k = 4) == 73

Answer: assert Solution().numberOfSubstrings(s = "abcabcabcabcabcabc", k = 2) == 120

Answer: assert Solution().numberOfSubstrings(s = "aaaaaabbbbbcccccdddddeeeee", k = 5) == 213

Answer: assert Solution().numberOfSubstrings(s = "aabbccddeeffgg", k = 2) == 85

Answer: assert Solution().numberOfSubstrings(s = "pppppppppppppppppppp", k = 15) == 21

Answer: assert Solution().numberOfSubstrings(s = "xyxyxyxyxy", k = 2) == 36

Answer: assert Solution().numberOfSubstrings(s = "xxyyzzxxyyzzxxyyzz", k = 3) == 78

Answer: assert Solution().numberOfSubstrings(s = "abcabcabcabc", k = 4) == 6

Answer: assert Solution().numberOfSubstrings(s = "aabbccddeeffgghhiijjkk", k = 2) == 221

Answer: assert Solution().numberOfSubstrings(s = "zzzzzzzzzzzzzzzzzzzzzz", k = 10) == 91

Answer: assert Solution().numberOfSubstrings(s = "hellohellohello", k = 3) == 45

Answer: assert Solution().numberOfSubstrings(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", k = 3) == 0

Answer: assert Solution().numberOfSubstrings(s = "ababababab", k = 2) == 36

Answer: assert Solution().numberOfSubstrings(s = "abcdefghijklmnopqrstuvwyxz", k = 1) == 351

Answer: assert Solution().numberOfSubstrings(s = "pppppppppppppppppppppppppp", k = 15) == 78

Answer: assert Solution().numberOfSubstrings(s = "qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq", k = 10) == 561

Answer: assert Solution().numberOfSubstrings(s = "aabbaaabbbaaabbaa", k = 3) == 100

Answer: assert Solution().numberOfSubstrings(s = "abababababababababababababababababababab", k = 5) == 528

Answer: assert Solution().numberOfSubstrings(s = "abcdefgabcdefg", k = 2) == 28

Answer: assert Solution().numberOfSubstrings(s = "aabbbccc", k = 3) == 15

Answer: assert Solution().numberOfSubstrings(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", k = 15) == 1953

Answer: assert Solution().numberOfSubstrings(s = "ababcabcab", k = 3) == 12

Answer: assert Solution().numberOfSubstrings(s = "aabbaaccc", k = 2) == 33

Answer: assert Solution().numberOfSubstrings(s = "abcdefghij", k = 1) == 55

Answer: assert Solution().numberOfSubstrings(s = "aaabbbcccdddeeefffggghhhiii", k = 3) == 301

Answer: assert Solution().numberOfSubstrings(s = "aabccba", k = 2) == 15

Answer: assert Solution().numberOfSubstrings(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", k = 1) == 1378

Answer: assert Solution().numberOfSubstrings(s = "aaabbbccc", k = 2) == 34

Answer: assert Solution().numberOfSubstrings(s = "aabbbccc", k = 2) == 26

Answer: assert Solution().numberOfSubstrings(s = "abcdefghij", k = 2) == 0

Answer: assert Solution().numberOfSubstrings(s = "abacabadabacabadabacaba", k = 2) == 221

Answer: assert Solution().numberOfSubstrings(s = "abcdabcdabcdabcd", k = 1) == 136

Answer: assert Solution().numberOfSubstrings(s = "mississippiissippi", k = 3) == 93

Answer: assert Solution().numberOfSubstrings(s = "aabbccdd", k = 2) == 25

Answer: assert Solution().numberOfSubstrings(s = "mnopqrstuvmnopqrstuvmnopqrstuvmnopqrstuvmnopqrstuvmnopqrstuvm", k = 5) == 231

Answer: assert Solution().numberOfSubstrings(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", k = 20) == 1128

Answer: assert Solution().numberOfSubstrings(s = "aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz", k = 4) == 0

Answer: assert Solution().numberOfSubstrings(s = "abcdefghijklmnopqrstuvwxyz", k = 2) == 0

Answer: assert Solution().numberOfSubstrings(s = "aaabbbcccdddeeefffggghhhhiii", k = 3) == 327

Answer: assert Solution().numberOfSubstrings(s = "abcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabc", k = 5) == 1485

Answer: assert Solution().numberOfSubstrings(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", k = 2) == 1301

Answer: assert Solution().numberOfSubstrings(s = "aabbbcccddd", k = 3) == 36

Answer: assert Solution().numberOfSubstrings(s = "xyzxyzxyzxyz", k = 3) == 21

Answer: assert Solution().numberOfSubstrings(s = "banana", k = 3) == 2

Answer: assert Solution().numberOfSubstrings(s = "xyzzyxzyzyxzyzxzyzxzyz", k = 2) == 200

Answer: assert Solution().numberOfSubstrings(s = "abacabadaba", k = 2) == 41

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 numberOfSubstrings(self, s: str, k: int) -> int:
        cnt = Counter()
        ans = l = 0
        for c in s:
            cnt[c] += 1
            while cnt[c] >= k:
                cnt[s[l]] -= 1
                l += 1
            ans += l
        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.
The factor score of an array is defined as the product of the LCM and GCD of all elements of that array.
Return the maximum factor score of nums after removing at most one element from it.
Note that both the LCM and GCD of a single number are the number itself, and the factor score of an empty array is 0.

Example 1:

Input: nums = [2,4,8,16]
Output: 64
Explanation:
On removing 2, the GCD of the rest of the elements is 4 while the LCM is 16, which gives a maximum factor score of 4 * 16 = 64.

Example 2:

Input: nums = [1,2,3,4,5]
Output: 60
Explanation:
The maximum factor score of 60 can be obtained without removing any elements.

Example 3:

Input: nums = [3]
Output: 9

Constraints:

1 <= nums.length <= 100
1 <= nums[i] <= 30

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

SOLUTION:

Question:
PROBLEM:
You are given an integer array nums.
The factor score of an array is defined as the product of the LCM and GCD of all elements of that array.
Return the maximum factor score of nums after removing at most one element from it.
Note that both the LCM and GCD of a single number are the number itself, and the factor score of an empty array is 0.

Example 1:

Input: nums = [2,4,8,16]
Output: 64
Explanation:
On removing 2, the GCD of the rest of the elements is 4 while the LCM is 16, which gives a maximum factor score of 4 * 16 = 64.

Example 2:

Input: nums = [1,2,3,4,5]
Output: 60
Explanation:
The maximum factor score of 60 can be obtained without removing any elements.

Example 3:

Input: nums = [3]
Output: 9

Constraints:

1 <= nums.length <= 100
1 <= nums[i] <= 30

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

SOLUTION:

assert Solution().maxScore(nums = [10,20,30]) == 600

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

assert Solution().maxScore(nums = [2,3,5,7,11]) == 2310

assert Solution().maxScore(nums = [12,15,18,21]) == 3780

assert Solution().maxScore(nums = [25,50,75,100]) == 7500

assert Solution().maxScore(nums = [30,15,10,5]) == 150

assert Solution().maxScore(nums = [25,10,5,1]) == 250

assert Solution().maxScore(nums = [11,22,33,44]) == 1452

assert Solution().maxScore(nums = [30,20,10,5]) == 600

assert Solution().maxScore(nums = [3]) == 9

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

assert Solution().maxScore(nums = [2,4,8,16]) == 64

assert Solution().maxScore(nums = [1,2,3,4,5]) == 60

assert Solution().maxScore(nums = [10,15,20,25]) == 1500

assert Solution().maxScore(nums = [7,14,28,56]) == 784

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

assert Solution().maxScore(nums = [2,6,18]) == 108

assert Solution().maxScore(nums = [6,12,18,24]) == 432

assert Solution().maxScore(nums = [100,50,25,10]) == 2500

assert Solution().maxScore(nums = [5,10,15,20]) == 300

assert Solution().maxScore(nums = [6,12,36,18]) == 216

assert Solution().maxScore(nums = [7,7,7,7]) == 49

assert Solution().maxScore(nums = [7,11,13]) == 1001

assert Solution().maxScore(nums = [7,14,21,28]) == 588

assert Solution().maxScore(nums = [7,14,28,35,70]) == 980

Answer: assert Solution().maxScore(nums = [10,20,30]) == 600

Answer: assert Solution().maxScore(nums = [100,200,300,400]) == 120000

Answer: assert Solution().maxScore(nums = [2,3,5,7,11,13]) == 30030

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

Answer: assert Solution().maxScore(nums = [2,3,5,7,11]) == 2310

Answer: assert Solution().maxScore(nums = [12,15,18,21]) == 3780

Answer: assert Solution().maxScore(nums = [25,50,75,100]) == 7500

Answer: assert Solution().maxScore(nums = [30,15,10,5]) == 150

Answer: assert Solution().maxScore(nums = [25,10,5,1]) == 250

Answer: assert Solution().maxScore(nums = [11,22,33,44]) == 1452

Answer: assert Solution().maxScore(nums = [30,20,10,5]) == 600

Answer: assert Solution().maxScore(nums = [3]) == 9

Answer: assert Solution().maxScore(nums = [29,28,27,26,25]) == 7125300

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

Answer: assert Solution().maxScore(nums = [2,4,8,16]) == 64

Answer: assert Solution().maxScore(nums = [1,2,3,4,5]) == 60

Answer: assert Solution().maxScore(nums = [10,15,20,25]) == 1500

Answer: assert Solution().maxScore(nums = [7,14,28,56]) == 784

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

Answer: assert Solution().maxScore(nums = [2,6,18]) == 108

Answer: assert Solution().maxScore(nums = [6,12,18,24]) == 432

Answer: assert Solution().maxScore(nums = [100,50,25,10]) == 2500

Answer: assert Solution().maxScore(nums = [5,10,15,20]) == 300

Answer: assert Solution().maxScore(nums = [6,12,36,18]) == 216

Answer: assert Solution().maxScore(nums = [7,7,7,7]) == 49

Answer: assert Solution().maxScore(nums = [7,11,13]) == 1001

Answer: assert Solution().maxScore(nums = [7,14,21,28]) == 588

Answer: assert Solution().maxScore(nums = [1023, 1024, 1025, 1026, 1027, 1028, 1029, 1030, 1031, 1032]) == 75902765337650830945766400

Answer: assert Solution().maxScore(nums = [21,42,63,84,105,126,147,168,189,210,231,252,273,294,315]) == 158918760

Answer: assert Solution().maxScore(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100]) == 5819814000

Answer: assert Solution().maxScore(nums = [7,14,21,28,35,42,49,56,63,70,77,84,91,98,105,112,119,126,133,140]) == 11406835440

Answer: assert Solution().maxScore(nums = [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]) == 123480

Answer: assert Solution().maxScore(nums = [11,22,33,44,55,66,77,88,99,110,121,132,143,154,165,176,187,198,209,220,231,242,253]) == 647861694480

Answer: assert Solution().maxScore(nums = [10, 20, 30, 40, 50, 60]) == 6000

Answer: assert Solution().maxScore(nums = [8,16,32,64,128,256]) == 4096

Answer: assert Solution().maxScore(nums = [17,34,51,68,85,102,119,136,153,170,187,204,221,238,255,272,289,306]) == 3540897360

Answer: assert Solution().maxScore(nums = [11,22,33,44,55,66,77,88,99]) == 304920

Answer: assert Solution().maxScore(nums = [4,8,12,16,20,24,28,32,36,40,44,48]) == 443520

Answer: assert Solution().maxScore(nums = [7,14,21,28,35,42]) == 2940

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

Answer: assert Solution().maxScore(nums = [2, 4, 8, 16, 32, 64, 128, 256, 512, 1024]) == 4096

Answer: assert Solution().maxScore(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29]) == 145568097675

Answer: assert Solution().maxScore(nums = [4,8,16,32,64,128,256,512,1024,2048,4096]) == 32768

Answer: assert Solution().maxScore(nums = [5,10,15,20,25,30,35,40,45,50]) == 63000

Answer: assert Solution().maxScore(nums = [24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240]) == 33522128640

Answer: assert Solution().maxScore(nums = [1,2,4,8,16,32,64,128,256,512]) == 1024

Answer: assert Solution().maxScore(nums = [7, 14, 21, 28, 35, 42, 49]) == 20580

Answer: assert Solution().maxScore(nums = [15, 30, 45, 60, 75, 90, 105, 120, 135, 150]) == 567000

Answer: assert Solution().maxScore(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30]) == 22680

Answer: assert Solution().maxScore(nums = [4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100]) == 428338310400

Answer: assert Solution().maxScore(nums = [5,10,15,20,25,30,35,40,45,50,55,60]) == 693000

Answer: assert Solution().maxScore(nums = [9,18,27,36,45,54,63,72,81,90,99,108,117,126,135]) == 29189160

Answer: assert Solution().maxScore(nums = [42,84,126,168,210,252,294,336,378,420,462,504,546,588,630]) == 635675040

Answer: assert Solution().maxScore(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]) == 232862364358497360900063316880507363070

Answer: assert Solution().maxScore(nums = [13,26,39,52,65,78,91,104,117,130,143,156,169,182,195,208]) == 121801680

Answer: assert Solution().maxScore(nums = [3,5,9,15,27,45]) == 405

Answer: assert Solution().maxScore(nums = [30, 60, 90, 120, 150, 180, 210, 240, 270, 300]) == 2268000

Answer: assert Solution().maxScore(nums = [8,16,24,32,40,48,56,64,72,80,88,96,104,112,120]) == 23063040

Answer: assert Solution().maxScore(nums = [21, 42, 63, 84, 105, 126, 147, 168, 189, 210, 231, 252, 273, 294, 315, 336, 357, 378, 399, 420]) == 102661518960

Answer: assert Solution().maxScore(nums = [23, 46, 69, 92, 115, 138, 161, 184, 207, 230, 253, 276, 299, 322, 345, 368, 391, 414, 437, 460]) == 123147264240

Answer: assert Solution().maxScore(nums = [11,22,33,44,55,66,77]) == 50820

Answer: assert Solution().maxScore(nums = [21,42,63,84,105,126,147,168,189,210]) == 1111320

Answer: assert Solution().maxScore(nums = [31,37,41,43,47,53,59,61,67,71,73,79,83,89,97]) == 356364340932671768233607909

Answer: assert Solution().maxScore(nums = [12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240]) == 33522128640

Answer: assert Solution().maxScore(nums = [8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120]) == 23063040

Answer: assert Solution().maxScore(nums = [15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225]) == 81081000

Answer: assert Solution().maxScore(nums = [10,20,30,40,50,60,70]) == 42000

Answer: assert Solution().maxScore(nums = [23, 46, 69, 92, 115, 138, 161, 184, 207, 230]) == 1333080

Answer: assert Solution().maxScore(nums = [8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160]) == 14898723840

Answer: assert Solution().maxScore(nums = [10,15,20,25,30]) == 1500

Answer: assert Solution().maxScore(nums = [3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60]) == 2095133040

Answer: assert Solution().maxScore(nums = [2, 3, 5, 7, 11, 13]) == 30030

Answer: assert Solution().maxScore(nums = [17, 34, 51, 68, 85, 102, 119, 136, 153, 170]) == 728280

Answer: assert Solution().maxScore(nums = [3,6,9,12,15,18,21,24,27,30,33]) == 249480

Answer: assert Solution().maxScore(nums = [4, 9, 16, 25, 36, 49, 64, 81, 100]) == 6350400

Answer: assert Solution().maxScore(nums = [25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300]) == 17325000

Answer: assert Solution().maxScore(nums = [15,25,35,45,55,65,75,85,95,105,115,125,135,145,155]) == 112815275698125

Answer: assert Solution().maxScore(nums = [25,50,75,100,125,150,175,200,225,250,275,300,325,350,375,400]) == 450450000

Answer: assert Solution().maxScore(nums = [2,4,8,16,32,64,128,256,512,1024]) == 4096

Answer: assert Solution().maxScore(nums = [8,12,24,36,48,60,72,84]) == 60480

Answer: assert Solution().maxScore(nums = [10,20,30,40,50,60,70,80,90,100]) == 252000

Answer: assert Solution().maxScore(nums = [23,46,69,92,115,138,161,184,207,230,253,276,299,322]) == 190630440

Answer: assert Solution().maxScore(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 360360

Answer: assert Solution().maxScore(nums = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]) == 6469693230

Answer: assert Solution().maxScore(nums = [25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100]) == 5819814000

Answer: assert Solution().maxScore(nums = [10, 20, 30, 40, 50]) == 6000

Answer: assert Solution().maxScore(nums = [13,26,39,52,65,78,91,104,117,130,143,156,169,182,195,208,221,234,247,260]) == 39341942640

Answer: assert Solution().maxScore(nums = [9,18,27,36,45,54,63,72,81,90,99,108]) == 2245320

Answer: assert Solution().maxScore(nums = [5,10,15,20,25,30,35,40,45,50,55,60,65,70,75]) == 9009000

Answer: assert Solution().maxScore(nums = [9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180]) == 18856197360

Answer: assert Solution().maxScore(nums = [29,58,87,116,145,174,203,232,261,290,319,348,377,406,435,464,493,522,551]) == 195778542960

Answer: assert Solution().maxScore(nums = [30,60,90,120,150,180,210,240,270,300,330,360]) == 24948000

Answer: assert Solution().maxScore(nums = [10,20,30,40,50,60,70,80,90,100,110,120]) == 2772000

Answer: assert Solution().maxScore(nums = [7,14,28,35,42,56]) == 5880

Answer: assert Solution().maxScore(nums = [7,14,28,35,70]) == 980

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

Answer: assert Solution().maxScore(nums = [12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96]) == 25945920

Answer: assert Solution().maxScore(nums = [101,202,303,404,505,606,707,808,909,1010,1111,1212,1313,1414,1515,1616]) == 7352064720

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

Answer: assert Solution().maxScore(nums = [15,30,45,60,75,90,105,120,135,150,165,180,195,210]) == 81081000

Answer: assert Solution().maxScore(nums = [10,15,20,25,30,35]) == 10500

Answer: assert Solution().maxScore(nums = [11,22,33,44,55,66,77,88,99,110,121,132]) == 3354120

Answer: assert Solution().maxScore(nums = [9, 18, 27, 36, 45, 54, 63, 72, 81]) == 204120

Answer: assert Solution().maxScore(nums = [9,18,27,36,45,54,63,72,81,90]) == 204120

Answer: assert Solution().maxScore(nums = [24, 48, 72, 96, 120, 144, 168, 192, 216, 240]) == 1451520

Answer: assert Solution().maxScore(nums = [7, 14, 28, 35, 42, 49, 56, 70]) == 41160

Answer: assert Solution().maxScore(nums = [3,6,9,12,15,18,21,24,27,30,33,36,39,42]) == 3243240

Answer: assert Solution().maxScore(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 252000

Answer: assert Solution().maxScore(nums = [17,34,51,68,85,102,119,136,153,170,187,204,221,238,255,272,289,306,323,340,357,374,391,408,425]) == 7736860731600

Answer: assert Solution().maxScore(nums = [13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]) == 998081369673384599460217379797297

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

Answer: assert Solution().maxScore(nums = [60,120,180,240,300,360,420,480,540,600]) == 9072000

Answer: assert Solution().maxScore(nums = [5, 10, 15, 20, 25, 30, 35, 40]) == 21000

Answer: assert Solution().maxScore(nums = [2,3,5,7,11,13,17,19,23,29]) == 6469693230

Answer: assert Solution().maxScore(nums = [12,24,36,48,60,72,84,96,108,120]) == 362880

Answer: assert Solution().maxScore(nums = [100,200,300,400,500,600,700,800,900,1000]) == 25200000

Answer: assert Solution().maxScore(nums = [29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10]) == 2329089562800

Answer: assert Solution().maxScore(nums = [19,38,57,76,95,114,133,152,171,190,209,228,247,266,285,304,323,342,361]) == 84038114160

Answer: assert Solution().maxScore(nums = [7,14,28,35,42]) == 2940

Answer: assert Solution().maxScore(nums = [12, 24, 36, 48, 60, 72, 84, 96, 108, 120]) == 362880

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 maxScore(self, nums: List[int]) -> int:
        n = len(nums)
        suf_gcd = [0] * (n + 1)
        suf_lcm = [0] * n + [1]
        for i in range(n - 1, -1, -1):
            suf_gcd[i] = gcd(suf_gcd[i + 1], nums[i])
            suf_lcm[i] = lcm(suf_lcm[i + 1], nums[i])
        ans = suf_gcd[0] * suf_lcm[0]
        pre_gcd, pre_lcm = 0, 1
        for i, x in enumerate(nums):
            ans = max(ans, gcd(pre_gcd, suf_gcd[i + 1]) * lcm(pre_lcm, suf_lcm[i + 1]))
            pre_gcd = gcd(pre_gcd, x)
            pre_lcm = lcm(pre_lcm, x)
        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 a string s and an integer t, representing the number of transformations to perform. In one transformation, every character in s is replaced according to the following rules:

If the character is 'z', replace it with the string "ab".
Otherwise, replace it with the next character in the alphabet. For example, 'a' is replaced with 'b', 'b' is replaced with 'c', and so on.

Return the length of the resulting string after exactly t transformations.
Since the answer may be very large, return it modulo 109 + 7.

Example 1:

Input: s = "abcyy", t = 2
Output: 7
Explanation:

First Transformation (t = 1):

'a' becomes 'b'
'b' becomes 'c'
'c' becomes 'd'
'y' becomes 'z'
'y' becomes 'z'
String after the first transformation: "bcdzz"

Second Transformation (t = 2):

'b' becomes 'c'
'c' becomes 'd'
'd' becomes 'e'
'z' becomes "ab"
'z' becomes "ab"
String after the second transformation: "cdeabab"

Final Length of the string: The string is "cdeabab", which has 7 characters.

Example 2:

Input: s = "azbk", t = 1
Output: 5
Explanation:

First Transformation (t = 1):

'a' becomes 'b'
'z' becomes "ab"
'b' becomes 'c'
'k' becomes 'l'
String after the first transformation: "babcl"

Final Length of the string: The string is "babcl", which has 5 characters.

Constraints:

1 <= s.length <= 105
s consists only of lowercase English letters.
1 <= t <= 105

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

SOLUTION:

Question:
PROBLEM:
You are given a string s and an integer t, representing the number of transformations to perform. In one transformation, every character in s is replaced according to the following rules:

If the character is 'z', replace it with the string "ab".
Otherwise, replace it with the next character in the alphabet. For example, 'a' is replaced with 'b', 'b' is replaced with 'c', and so on.

Return the length of the resulting string after exactly t transformations.
Since the answer may be very large, return it modulo 109 + 7.

Example 1:

Input: s = "abcyy", t = 2
Output: 7
Explanation:

First Transformation (t = 1):

'a' becomes 'b'
'b' becomes 'c'
'c' becomes 'd'
'y' becomes 'z'
'y' becomes 'z'
String after the first transformation: "bcdzz"

Second Transformation (t = 2):

'b' becomes 'c'
'c' becomes 'd'
'd' becomes 'e'
'z' becomes "ab"
'z' becomes "ab"
String after the second transformation: "cdeabab"

Final Length of the string: The string is "cdeabab", which has 7 characters.

Example 2:

Input: s = "azbk", t = 1
Output: 5
Explanation:

First Transformation (t = 1):

'a' becomes 'b'
'z' becomes "ab"
'b' becomes 'c'
'k' becomes 'l'
String after the first transformation: "babcl"

Final Length of the string: The string is "babcl", which has 5 characters.

Constraints:

1 <= s.length <= 105
s consists only of lowercase English letters.
1 <= t <= 105

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

SOLUTION:

assert Solution().lengthAfterTransformations(s = "abcd", t = 5) == 4

assert Solution().lengthAfterTransformations(s = "abcdefghijklmnopqrstuvwxyz", t = 5) == 31

assert Solution().lengthAfterTransformations(s = "azbk", t = 1) == 5

assert Solution().lengthAfterTransformations(s = "abcdef", t = 5) == 6

assert Solution().lengthAfterTransformations(s = "abcdefg", t = 5) == 7

assert Solution().lengthAfterTransformations(s = "abcyy", t = 2) == 7

assert Solution().lengthAfterTransformations(s = "a", t = 100000) == 413966020

assert Solution().lengthAfterTransformations(s = "zzzz", t = 3) == 8

assert Solution().lengthAfterTransformations(s = "zzz", t = 3) == 6

assert Solution().lengthAfterTransformations(s = "yzxyzz", t = 5) == 12

assert Solution().lengthAfterTransformations(s = "zyxwvutsrqponmlkjihgfedcba", t = 50000) == 970042322

assert Solution().lengthAfterTransformations(s = "zzzzzzzzzz", t = 10) == 20

assert Solution().lengthAfterTransformations(s = "ababababab", t = 100000) == 249107450

assert Solution().lengthAfterTransformations(s = "aaaabbbbccccddddeeeeffffgggghhhhiiii", t = 50000) == 584847311

assert Solution().lengthAfterTransformations(s = "zzzzzzzzzz", t = 7) == 20

assert Solution().lengthAfterTransformations(s = "abczyz", t = 100000) == 717149713

assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = 10000) == 295436100

assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzz", t = 10) == 52

assert Solution().lengthAfterTransformations(s = "zazazazazazazazazaza", t = 20) == 30

assert Solution().lengthAfterTransformations(s = "abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz", t = 1) == 54

assert Solution().lengthAfterTransformations(s = "zyxwvutsrqponmlkjihgfedcba", t = 15) == 41

assert Solution().lengthAfterTransformations(s = "abcdxyz", t = 100000) == 673034982

assert Solution().lengthAfterTransformations(s = "aaaazzz", t = 5) == 10

assert Solution().lengthAfterTransformations(s = "abcdefghijklmnopqrstuvwxyz", t = 100000) == 704103930

assert Solution().lengthAfterTransformations(s = "azazazazaz", t = 5) == 15

assert Solution().lengthAfterTransformations(s = "z", t = 1000000) == 560162355

assert Solution().lengthAfterTransformations(s = "zyx", t = 100) == 48

assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = 50000) == 57514287

assert Solution().lengthAfterTransformations(s = "zzzzzzzzzz", t = 50000) == 811502863

assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = 100000) == 249063434

assert Solution().lengthAfterTransformations(s = "mnbvcxzlkjhgfdsapoiuytrewq", t = 50) == 101

assert Solution().lengthAfterTransformations(s = "zabzabzabz", t = 10) == 14

assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzz", t = 100000) == 327364041

assert Solution().lengthAfterTransformations(s = "azazazazaz", t = 50) == 30

assert Solution().lengthAfterTransformations(s = "zyxwvutsrqponmlkjihgfedcba", t = 1) == 27

assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = 10000) == 850623003

assert Solution().lengthAfterTransformations(s = "zyxwvutsrqponmlkjihgfedcba", t = 10) == 36

assert Solution().lengthAfterTransformations(s = "bzzzzzzzzz", t = 50000) == 35738956

assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = 100000) == 14161613

assert Solution().lengthAfterTransformations(s = "zzzzz", t = 10) == 10

assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = 2) == 64

assert Solution().lengthAfterTransformations(s = "aaaaaaaaaaaabbbbbbbbbbbbbbcccccccccccc", t = 10) == 38

assert Solution().lengthAfterTransformations(s = "abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz", t = 100000) == 408207853

assert Solution().lengthAfterTransformations(s = "abzabzabzabz", t = 3) == 16

assert Solution().lengthAfterTransformations(s = "zyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyx", t = 25000) == 102001027

assert Solution().lengthAfterTransformations(s = "yyyyyyyyyy", t = 10) == 20

assert Solution().lengthAfterTransformations(s = "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaa", t = 1) == 30

assert Solution().lengthAfterTransformations(s = "zzzazazazzzz", t = 10) == 21

assert Solution().lengthAfterTransformations(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", t = 100000) == 408207853

assert Solution().lengthAfterTransformations(s = "abcdz", t = 100) == 60

assert Solution().lengthAfterTransformations(s = "abcdefghijklmnopqrstuvwxyz", t = 26) == 53

assert Solution().lengthAfterTransformations(s = "abxyzz", t = 20) == 10

assert Solution().lengthAfterTransformations(s = "abcdefghijklmnopqrstuvwxyz", t = 1) == 27

assert Solution().lengthAfterTransformations(s = "abcdefghijklmnopqrstuvwxyz", t = 10) == 36

assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = 1) == 64

assert Solution().lengthAfterTransformations(s = "abzabzabz", t = 10) == 12

assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = 100000) == 451895758

assert Solution().lengthAfterTransformations(s = "aaaaaaaaaa", t = 100000) == 139660172

assert Solution().lengthAfterTransformations(s = "bababababa", t = 20) == 10

assert Solution().lengthAfterTransformations(s = "zaabccdd", t = 5) == 9

assert Solution().lengthAfterTransformations(s = "zyzzyx", t = 5) == 12

assert Solution().lengthAfterTransformations(s = "abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz", t = 100) == 792

assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzz", t = 1) == 52

assert Solution().lengthAfterTransformations(s = "abzaz", t = 10) == 7

assert Solution().lengthAfterTransformations(s = "bzz", t = 10) == 5

assert Solution().lengthAfterTransformations(s = "yzyzyzyzyz", t = 7) == 20

assert Solution().lengthAfterTransformations(s = "zzzz", t = 20) == 8

assert Solution().lengthAfterTransformations(s = "abczzzzyx", t = 50) == 33

assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = 5000) == 333013051

assert Solution().lengthAfterTransformations(s = "zzzzzzzzzz", t = 100000) == 202832324

assert Solution().lengthAfterTransformations(s = "azazazazaz", t = 20) == 15

assert Solution().lengthAfterTransformations(s = "bbbbbbbbbbbbbbbbbb", t = 5000) == 282316300

assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = 99999) == 941360394

assert Solution().lengthAfterTransformations(s = "zyzx", t = 5) == 8

assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = 100000) == 309456157

assert Solution().lengthAfterTransformations(s = "abababababababababababababababab", t = 25000) == 651990487

assert Solution().lengthAfterTransformations(s = "z", t = 100000) == 820283238

assert Solution().lengthAfterTransformations(s = "aaaaaaaaaazzzzzzzzzz", t = 50) == 60

assert Solution().lengthAfterTransformations(s = "zyxwvutsrqponmlkjihgfedcba", t = 100000) == 704103930

assert Solution().lengthAfterTransformations(s = "aazzbbyy", t = 20) == 12

assert Solution().lengthAfterTransformations(s = "zyzzyzzyzzyzzyzzyzzyzzyzzyzzyz", t = 50000) == 266826870

assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = 50000) == 796809149

assert Solution().lengthAfterTransformations(s = "zabcyz", t = 5) == 9

assert Solution().lengthAfterTransformations(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", t = 50000) == 940084637

assert Solution().lengthAfterTransformations(s = "zzzzzzzzzz", t = 5) == 20

assert Solution().lengthAfterTransformations(s = "abcdefghijklmnopqrstuvwxyz", t = 1000) == 836719952

assert Solution().lengthAfterTransformations(s = "mnbvcxzlkjhgfdsapoiuytrewq", t = 100) == 396

Answer: assert Solution().lengthAfterTransformations(s = "abcd", t = 5) == 4

Answer: assert Solution().lengthAfterTransformations(s = "abcdefghijklmnopqrstuvwxyz", t = 5) == 31

Answer: assert Solution().lengthAfterTransformations(s = "azbk", t = 1) == 5

Answer: assert Solution().lengthAfterTransformations(s = "abcdef", t = 5) == 6

Answer: assert Solution().lengthAfterTransformations(s = "abcdefg", t = 5) == 7

Answer: assert Solution().lengthAfterTransformations(s = "abcyy", t = 2) == 7

Answer: assert Solution().lengthAfterTransformations(s = "a", t = 100000) == 413966020

Answer: assert Solution().lengthAfterTransformations(s = "zzzz", t = 3) == 8

Answer: assert Solution().lengthAfterTransformations(s = "zzz", t = 3) == 6

Answer: assert Solution().lengthAfterTransformations(s = "yzxyzz", t = 5) == 12

Answer: assert Solution().lengthAfterTransformations(s = "zyxwvutsrqponmlkjihgfedcba", t = 50000) == 970042322

Answer: assert Solution().lengthAfterTransformations(s = "zzzzzzzzzz", t = 10) == 20

Answer: assert Solution().lengthAfterTransformations(s = "ababababab", t = 100000) == 249107450

Answer: assert Solution().lengthAfterTransformations(s = "aaaabbbbccccddddeeeeffffgggghhhhiiii", t = 50000) == 584847311

Answer: assert Solution().lengthAfterTransformations(s = "zzzzzzzzzz", t = 7) == 20

Answer: assert Solution().lengthAfterTransformations(s = "abczyz", t = 100000) == 717149713

Answer: assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = 10000) == 295436100

Answer: assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzz", t = 10) == 52

Answer: assert Solution().lengthAfterTransformations(s = "zazazazazazazazazaza", t = 20) == 30

Answer: assert Solution().lengthAfterTransformations(s = "abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz", t = 1) == 54

Answer: assert Solution().lengthAfterTransformations(s = "zyxwvutsrqponmlkjihgfedcba", t = 15) == 41

Answer: assert Solution().lengthAfterTransformations(s = "abcdxyz", t = 100000) == 673034982

Answer: assert Solution().lengthAfterTransformations(s = "aaaazzz", t = 5) == 10

Answer: assert Solution().lengthAfterTransformations(s = "abcdefghijklmnopqrstuvwxyz", t = 100000) == 704103930

Answer: assert Solution().lengthAfterTransformations(s = "azazazazaz", t = 5) == 15

Answer: assert Solution().lengthAfterTransformations(s = "z", t = 1000000) == 560162355

Answer: assert Solution().lengthAfterTransformations(s = "zyx", t = 100) == 48

Answer: assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = 50000) == 57514287

Answer: assert Solution().lengthAfterTransformations(s = "zzzzzzzzzz", t = 50000) == 811502863

Answer: assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = 100000) == 249063434

Answer: assert Solution().lengthAfterTransformations(s = "mnbvcxzlkjhgfdsapoiuytrewq", t = 50) == 101

Answer: assert Solution().lengthAfterTransformations(s = "zabzabzabz", t = 10) == 14

Answer: assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzz", t = 100000) == 327364041

Answer: assert Solution().lengthAfterTransformations(s = "azazazazaz", t = 50) == 30

Answer: assert Solution().lengthAfterTransformations(s = "zyxwvutsrqponmlkjihgfedcba", t = 1) == 27

Answer: assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = 10000) == 850623003

Answer: assert Solution().lengthAfterTransformations(s = "zyxwvutsrqponmlkjihgfedcba", t = 10) == 36

Answer: assert Solution().lengthAfterTransformations(s = "bzzzzzzzzz", t = 50000) == 35738956

Answer: assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = 100000) == 14161613

Answer: assert Solution().lengthAfterTransformations(s = "zzzzz", t = 10) == 10

Answer: assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = 2) == 64

Answer: assert Solution().lengthAfterTransformations(s = "aaaaaaaaaaaabbbbbbbbbbbbbbcccccccccccc", t = 10) == 38

Answer: assert Solution().lengthAfterTransformations(s = "abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz", t = 100000) == 408207853

Answer: assert Solution().lengthAfterTransformations(s = "abzabzabzabz", t = 3) == 16

Answer: assert Solution().lengthAfterTransformations(s = "zyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyx", t = 25000) == 102001027

Answer: assert Solution().lengthAfterTransformations(s = "yyyyyyyyyy", t = 10) == 20

Answer: assert Solution().lengthAfterTransformations(s = "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaa", t = 1) == 30

Answer: assert Solution().lengthAfterTransformations(s = "zzzazazazzzz", t = 10) == 21

Answer: assert Solution().lengthAfterTransformations(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", t = 100000) == 408207853

Answer: assert Solution().lengthAfterTransformations(s = "abcdz", t = 100) == 60

Answer: assert Solution().lengthAfterTransformations(s = "abcdefghijklmnopqrstuvwxyz", t = 26) == 53

Answer: assert Solution().lengthAfterTransformations(s = "abxyzz", t = 20) == 10

Answer: assert Solution().lengthAfterTransformations(s = "abcdefghijklmnopqrstuvwxyz", t = 1) == 27

Answer: assert Solution().lengthAfterTransformations(s = "abcdefghijklmnopqrstuvwxyz", t = 10) == 36

Answer: assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = 1) == 64

Answer: assert Solution().lengthAfterTransformations(s = "abzabzabz", t = 10) == 12

Answer: assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = 100000) == 451895758

Answer: assert Solution().lengthAfterTransformations(s = "aaaaaaaaaa", t = 100000) == 139660172

Answer: assert Solution().lengthAfterTransformations(s = "bababababa", t = 20) == 10

Answer: assert Solution().lengthAfterTransformations(s = "zaabccdd", t = 5) == 9

Answer: assert Solution().lengthAfterTransformations(s = "zyzzyx", t = 5) == 12

Answer: assert Solution().lengthAfterTransformations(s = "abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz", t = 100) == 792

Answer: assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzz", t = 1) == 52

Answer: assert Solution().lengthAfterTransformations(s = "abzaz", t = 10) == 7

Answer: assert Solution().lengthAfterTransformations(s = "bzz", t = 10) == 5

Answer: assert Solution().lengthAfterTransformations(s = "yzyzyzyzyz", t = 7) == 20

Answer: assert Solution().lengthAfterTransformations(s = "zzzz", t = 20) == 8

Answer: assert Solution().lengthAfterTransformations(s = "abczzzzyx", t = 50) == 33

Answer: assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = 5000) == 333013051

Answer: assert Solution().lengthAfterTransformations(s = "zzzzzzzzzz", t = 100000) == 202832324

Answer: assert Solution().lengthAfterTransformations(s = "azazazazaz", t = 20) == 15

Answer: assert Solution().lengthAfterTransformations(s = "bbbbbbbbbbbbbbbbbb", t = 5000) == 282316300

Answer: assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = 99999) == 941360394

Answer: assert Solution().lengthAfterTransformations(s = "zyzx", t = 5) == 8

Answer: assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = 100000) == 309456157

Answer: assert Solution().lengthAfterTransformations(s = "abababababababababababababababab", t = 25000) == 651990487

Answer: assert Solution().lengthAfterTransformations(s = "z", t = 100000) == 820283238

Answer: assert Solution().lengthAfterTransformations(s = "aaaaaaaaaazzzzzzzzzz", t = 50) == 60

Answer: assert Solution().lengthAfterTransformations(s = "zyxwvutsrqponmlkjihgfedcba", t = 100000) == 704103930

Answer: assert Solution().lengthAfterTransformations(s = "aazzbbyy", t = 20) == 12

Answer: assert Solution().lengthAfterTransformations(s = "zyzzyzzyzzyzzyzzyzzyzzyzzyzzyz", t = 50000) == 266826870

Answer: assert Solution().lengthAfterTransformations(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = 50000) == 796809149

Answer: assert Solution().lengthAfterTransformations(s = "zabcyz", t = 5) == 9

Answer: assert Solution().lengthAfterTransformations(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", t = 50000) == 940084637

Answer: assert Solution().lengthAfterTransformations(s = "zzzzzzzzzz", t = 5) == 20

Answer: assert Solution().lengthAfterTransformations(s = "abcdefghijklmnopqrstuvwxyz", t = 1000) == 836719952

Answer: assert Solution().lengthAfterTransformations(s = "mnbvcxzlkjhgfdsapoiuytrewq", t = 100) == 396

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 lengthAfterTransformations(self, s: str, t: int) -> int:
    MOD = 1_000_000_007
    count = [0] * 26

    for c in s:
      count[ord(c) - ord('a')] += 1

    for _ in range(t):
      newCount = [0] * 26
      # 'a' -> 'b', 'b' -> 'c', ..., 'y' -> 'z'
      for i in range(25):
        newCount[i + 1] = count[i]
      # 'z' -> 'ab'
      newCount[0] = count[25]
      newCount[1] = (newCount[1] + count[25]) % MOD
      count = newCount

    return sum(count) % MOD