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 two strings s and t, both of which are anagrams of each other, and an integer k.
Your task is to determine whether it is possible to split the string s into k equal-sized substrings, rearrange the substrings, and concatenate them in any order to create a new string that matches the given string t.
Return true if this is possible, otherwise, return false.
An anagram is a word or phrase formed by rearranging the letters of a different word or phrase, using all the original letters exactly once.
A substring is a contiguous non-empty sequence of characters within a string.

Example 1:

Input: s = "abcd", t = "cdab", k = 2
Output: true
Explanation:

Split s into 2 substrings of length 2: ["ab", "cd"].
Rearranging these substrings as ["cd", "ab"], and then concatenating them results in "cdab", which matches t.

Example 2:

Input: s = "aabbcc", t = "bbaacc", k = 3
Output: true
Explanation:

Split s into 3 substrings of length 2: ["aa", "bb", "cc"].
Rearranging these substrings as ["bb", "aa", "cc"], and then concatenating them results in "bbaacc", which matches t.

Example 3:

Input: s = "aabbcc", t = "bbaacc", k = 2
Output: false
Explanation:

Split s into 2 substrings of length 3: ["aab", "bcc"].
These substrings cannot be rearranged to form t = "bbaacc", so the output is false.

Constraints:

1 <= s.length == t.length <= 2 * 105
1 <= k <= s.length
s.length is divisible by k.
s and t consist only of lowercase English letters.
The input is generated such that s and t are anagrams of each other.

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

SOLUTION:

Question:
PROBLEM:
You are given two strings s and t, both of which are anagrams of each other, and an integer k.
Your task is to determine whether it is possible to split the string s into k equal-sized substrings, rearrange the substrings, and concatenate them in any order to create a new string that matches the given string t.
Return true if this is possible, otherwise, return false.
An anagram is a word or phrase formed by rearranging the letters of a different word or phrase, using all the original letters exactly once.
A substring is a contiguous non-empty sequence of characters within a string.

Example 1:

Input: s = "abcd", t = "cdab", k = 2
Output: true
Explanation:

Split s into 2 substrings of length 2: ["ab", "cd"].
Rearranging these substrings as ["cd", "ab"], and then concatenating them results in "cdab", which matches t.

Example 2:

Input: s = "aabbcc", t = "bbaacc", k = 3
Output: true
Explanation:

Split s into 3 substrings of length 2: ["aa", "bb", "cc"].
Rearranging these substrings as ["bb", "aa", "cc"], and then concatenating them results in "bbaacc", which matches t.

Example 3:

Input: s = "aabbcc", t = "bbaacc", k = 2
Output: false
Explanation:

Split s into 2 substrings of length 3: ["aab", "bcc"].
These substrings cannot be rearranged to form t = "bbaacc", so the output is false.

Constraints:

1 <= s.length == t.length <= 2 * 105
1 <= k <= s.length
s.length is divisible by k.
s and t consist only of lowercase English letters.
The input is generated such that s and t are anagrams of each other.

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

SOLUTION:

assert Solution().isPossibleToRearrange(s = "abcd", t = "cdab", k = 2) == True

assert Solution().isPossibleToRearrange(s = "abcdefg", t = "gfedcba", k = 1) == False

assert Solution().isPossibleToRearrange(s = "abcdefg", t = "gfedcba", k = 7) == True

assert Solution().isPossibleToRearrange(s = "aabbcc", t = "bbaacc", k = 3) == True

assert Solution().isPossibleToRearrange(s = "abcabcabc", t = "bcbcbcbca", k = 3) == False

assert Solution().isPossibleToRearrange(s = "aabbcc", t = "bbaacc", k = 2) == False

assert Solution().isPossibleToRearrange(s = "abacabad", t = "dcabcdab", k = 2) == False

assert Solution().isPossibleToRearrange(s = "abcdefghijabcdefghijabcdefghij", t = "fedcbafedcbafedcba", k = 3) == False

assert Solution().isPossibleToRearrange(s = "xyzxyzxyzxyz", t = "zyxzyxzyxzyx", k = 4) == False

assert Solution().isPossibleToRearrange(s = "xyzyxzyzyzxzyzyz", t = "zyzyzyzyzyzyzyzx", k = 7) == False

assert Solution().isPossibleToRearrange(s = "abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz", t = "zyxwvutsrqponmlkjihgfedcbazyxwvutsrqponmlkjihgfedcba", k = 26) == False

assert Solution().isPossibleToRearrange(s = "abcdefghijabcdefghijabcdefghij", t = "abcdefghijabcdefghijabcdefghij", k = 3) == True

assert Solution().isPossibleToRearrange(s = "abababababab", t = "babababababa", k = 2) == False

assert Solution().isPossibleToRearrange(s = "aaabbbccc", t = "bbbaaacc", k = 3) == False

assert Solution().isPossibleToRearrange(s = "mississippiissi", t = "ssissimipissi", k = 5) == False

assert Solution().isPossibleToRearrange(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", t = "zzzyyxxwwvvuuttssrrqqppoonnmmllkkjjiihhggffeeeeddccbbaa", k = 13) == False

assert Solution().isPossibleToRearrange(s = "zzyyxxwwvvuuttssrrqqppoonnmmlkkjjiihhaaggeeccbb", t = "bcdeeegghhiikkmnnooppqqrrssttuuvvwwxxyyzz", k = 26) == False

assert Solution().isPossibleToRearrange(s = "abcdabcdabcdabcdabcdabcd", t = "dddddddcccccbbbbaaaaaa", k = 6) == False

assert Solution().isPossibleToRearrange(s = "mississippiissim", t = "simississippiiss", k = 6) == False

assert Solution().isPossibleToRearrange(s = "lkjlkjlkjlkjlkjlkjlkjlkj", t = "llllkkkkjjjjllllkkkkjjjjllllkkkkjjjj", k = 16) == True

assert Solution().isPossibleToRearrange(s = "aaaaaaaaaaaaaaaaaaaaaaaaaa", t = "aaaaaaaaaaaaaaaaaaaaaaaaaa", k = 10) == True

assert Solution().isPossibleToRearrange(s = "mmmmmmmmmmnnnnnnnn", t = "nnnnnnnnnnaaaaaaaaaa", k = 5) == False

assert Solution().isPossibleToRearrange(s = "abacabadabacabad", t = "badabacabadaba", k = 4) == False

assert Solution().isPossibleToRearrange(s = "aaabbbcccdddeeefffggghhh", t = "hgggfffeeedddcccbbaaa", k = 3) == False

assert Solution().isPossibleToRearrange(s = "aabbccddeeffgghhiijjkkllmmpqrs", t = "srqpmlkjihgfedcbazyxwvuts", k = 26) == False

assert Solution().isPossibleToRearrange(s = "xyzxyzxyzxyzxyzxyz", t = "zyxzyxzyxzyxzyxzyx", k = 6) == False

assert Solution().isPossibleToRearrange(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", t = "zzzyyxxwwvvuuttrrssqqppoonnmmllkkjjiihhggffeeeeddccbbaa", k = 25) == False

assert Solution().isPossibleToRearrange(s = "aaaabbbbccccdddd", t = "abcdabcdabcdabcd", k = 4) == False

assert Solution().isPossibleToRearrange(s = "mnopqrsmnopqrsmnopqrsmnopqrsmnopqrs", t = "smnopqrsmnopqrsmnopqrsmnopqrsmnopqrs", k = 10) == False

assert Solution().isPossibleToRearrange(s = "aaaabbbbccccdddd", t = "ddddccccbbbbaaaa", k = 4) == True

assert Solution().isPossibleToRearrange(s = "aabbbccddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqqrrrrssssttttuuuuvvvvwwwwxxxxxyyyyyzzzzz", t = "zzzzzyyyyyxxxxwwwwvvvvuuuuttttsssrrrrqqqqpppooonnnmmmlllkkkjjjiiihhhgggfffdddccbbbaaa", k = 26) == False

assert Solution().isPossibleToRearrange(s = "aaaabbbbccccddddeeeeffffgggghhhhiiii", t = "ihgfedcbihgfedcbihgfedcbihgfedcb", k = 5) == False

assert Solution().isPossibleToRearrange(s = "qwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnm", t = "mnbvcxzlkjhgfdsapoiuytrewqmnbvcxzlkjhgfdsapoiuytrew", k = 26) == False

assert Solution().isPossibleToRearrange(s = "aaaaaaabbbbbbbcccccc", t = "abcabcabcabcabcabcabcabc", k = 12) == True

assert Solution().isPossibleToRearrange(s = "abcdefghijklmnopqrstuabcdefghijklmnopqrstu", t = "utsrqponmlkjihgfedcbautsrqponmlkjihgfedcba", k = 10) == False

assert Solution().isPossibleToRearrange(s = "abacabadabacaba", t = "acaabbaadabacba", k = 3) == False

assert Solution().isPossibleToRearrange(s = "abcdeabcdeabcdeabcdeabcdeabcde", t = "deabcdeabcdeabcdeabcdeabcdeabc", k = 6) == False

assert Solution().isPossibleToRearrange(s = "abcdefgihjklmnopqrstuvwxyz", t = "zyxwvutsrqponmlkjihgfedcba", k = 26) == True

assert Solution().isPossibleToRearrange(s = "abcdefghijklmnopqrstuv", t = "ponmlkjihgfedcbazyxwvutsr", k = 10) == False

assert Solution().isPossibleToRearrange(s = "abcdefghijklmnop", t = "ponmlkjihgfedcba", k = 4) == False

assert Solution().isPossibleToRearrange(s = "abacabadabacabad", t = "daabcbcadabcadba", k = 4) == False

assert Solution().isPossibleToRearrange(s = "aabbccddeeff", t = "feeddcbaab", k = 2) == False

assert Solution().isPossibleToRearrange(s = "aaaabbbbccccddddeeeeffffgggghhhhiiiijjjjkkkkllllmmmmnnnnoooo", t = "ooooooooonnnnnmmmmllllkkkkjjjjiiiijjjjhhhhggggeeegfffeeeeddddddccccbbbbaaaa", k = 4) == False

assert Solution().isPossibleToRearrange(s = "zzzzzzzzzzzzzzzzzzzz", t = "zzzzzzzzzzzzzzzzzzzz", k = 5) == True

assert Solution().isPossibleToRearrange(s = "abcabcabcabc", t = "cccbbbaaaabc", k = 3) == False

assert Solution().isPossibleToRearrange(s = "nnnnoooommmmpppp", t = "nopmnopmnopmno", k = 4) == False

assert Solution().isPossibleToRearrange(s = "abcdefghijabcdefghij", t = "fedcbafedcbafedcba", k = 10) == False

assert Solution().isPossibleToRearrange(s = "abcdabcdabcdabcd", t = "ddddccccbbbbaaaa", k = 4) == False

assert Solution().isPossibleToRearrange(s = "abcabcabcabcabcabcabcabc", t = "cbacbacbacbacbacbacbacbacbacba", k = 4) == False

assert Solution().isPossibleToRearrange(s = "aaaaabbbbccccc", t = "bbbbbcccccddddd", k = 3) == False

assert Solution().isPossibleToRearrange(s = "aaaabbbbccccddddeeeeffffgggghhhh", t = "abcdefghabcdefghabcdefghabcdefgh", k = 8) == False

assert Solution().isPossibleToRearrange(s = "xyzxyzxyzxyz", t = "zyxzyxzyxzyx", k = 3) == False

assert Solution().isPossibleToRearrange(s = "abcdefabcdefabcdefabcdefabcdefabcdef", t = "fedcbafedcbafedcbafedcbafedcba", k = 18) == False

assert Solution().isPossibleToRearrange(s = "abcdefghijklmnopqrstuvwxyz", t = "zyxwvutsrqponmlkjihgfedcba", k = 26) == True

assert Solution().isPossibleToRearrange(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", t = "zzyyxxwwvvuuttrrssqqppoonnmmllkkjjiihhggffeeeeddccbbaa", k = 26) == False

assert Solution().isPossibleToRearrange(s = "mnopqrstuvwxyzabcdefghijkl", t = "abcdefghijklmnopqrstuvwxyz", k = 13) == True

assert Solution().isPossibleToRearrange(s = "abcdefghijabcdefghij", t = "jihgfedcbajihgfedcba", k = 10) == False

assert Solution().isPossibleToRearrange(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", k = 26) == True

assert Solution().isPossibleToRearrange(s = "mmmmnnnnooooppppqqqqrrrrssssttttuuuuvvvvwwwwxxxx", t = "xxxxxxxxwwwwvvvvuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu", k = 20) == False

assert Solution().isPossibleToRearrange(s = "abcdefghabcdefghabcdefghabcdefgh", t = "ddddccccbbbbaaaaeeeeffffffff", k = 16) == False

assert Solution().isPossibleToRearrange(s = "xyxyxyxyxyxy", t = "yxyxyxyxyxyx", k = 3) == False

assert Solution().isPossibleToRearrange(s = "aaaaaaaaaaabbbbbbbbbbbccccccccccdddddddddd", t = "bbbbbbbbbbbbaaaaaaaaaacccccccdddddddddd", k = 10) == False

assert Solution().isPossibleToRearrange(s = "aaaaaaaaaabbbbbbbbccccccccdddddddd", t = "ddddddddccccccccbbbbbbbbaaaaaaaa", k = 8) == False

assert Solution().isPossibleToRearrange(s = "zzzzzzzzzzzzzzzzzzzzzzzz", t = "zzzzzzzzzzzzzzzzzzzzzzzz", k = 1) == True

assert Solution().isPossibleToRearrange(s = "kkkkkkkkkk", t = "kkkkkkkkkk", k = 5) == True

assert Solution().isPossibleToRearrange(s = "abcdefabcdefabcdefabcdef", t = "aaaabbbbccccddddeeeeffff", k = 8) == False

assert Solution().isPossibleToRearrange(s = "abcabcabcabcabcabc", t = "cbaabcabcabcabcabc", k = 4) == False

assert Solution().isPossibleToRearrange(s = "abababababababababababababababab", t = "babababababababababababababababa", k = 2) == False

assert Solution().isPossibleToRearrange(s = "abcdefghijabcdefghijabcdefghij", t = "abcabcabcabcabcabcabcabcabcabcdeedefefefefefghighighighi", k = 15) == False

assert Solution().isPossibleToRearrange(s = "racecaracecaracecar", t = "racecaracecaracecar", k = 3) == True

assert Solution().isPossibleToRearrange(s = "aabbccddeeffgghhiijjkk", t = "jikkhhggffeeddccbbaa", k = 11) == False

assert Solution().isPossibleToRearrange(s = "xyzxyzxyzxyzxyzxyzxyzxyz", t = "zyxzyxzyxzyxzyxzyxzyxzyxzyx", k = 3) == False

assert Solution().isPossibleToRearrange(s = "thisisanexampleofalongstringthatweneedtosplit", t = "stingthatweneedtosplitthisisanexampleofalon", k = 7) == False

assert Solution().isPossibleToRearrange(s = "repeatthispatternrepeatthispatternrepeatthispattern", t = "ternpatrepeaternpatrepeaternpatrepeaternpat", k = 9) == False

assert Solution().isPossibleToRearrange(s = "abcdefabcdefabcdefabcdef", t = "fabcdfabcdfabcdfabcd", k = 8) == False

assert Solution().isPossibleToRearrange(s = "abcdefghijklmnopabcdefghijklmnop", t = "pponmlkjihgfedcbazyxwvutsrqponmlkjihgfedcba", k = 16) == False

assert Solution().isPossibleToRearrange(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", t = "zzzyyxxwwvvuuttrrssqqppoonnmmllkkjjiihhggffeeeeddccbbaa", k = 13) == False

assert Solution().isPossibleToRearrange(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", k = 26) == True

assert Solution().isPossibleToRearrange(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", k = 20) == True

assert Solution().isPossibleToRearrange(s = "abcdefabcdefabcdefabcdefabcdef", t = "fedcbafedcbafedcbafedcba", k = 5) == False

assert Solution().isPossibleToRearrange(s = "abacabadabacabad", t = "aabbccdaaabbccda", k = 4) == False

assert Solution().isPossibleToRearrange(s = "abcabcabcabcabcabc", t = "cabacbacbacbacba", k = 6) == False

assert Solution().isPossibleToRearrange(s = "nnnnoooommmm", t = "mmmmnnnnoooo", k = 3) == True

assert Solution().isPossibleToRearrange(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", k = 26) == True

assert Solution().isPossibleToRearrange(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", k = 1) == True

assert Solution().isPossibleToRearrange(s = "aabbaabbaabbaabbaabbaabbaabbaabbaabbaabb", t = "bbaabbaabbaabbaabbaabbaabbaabbaabbaabbaa", k = 10) == False

assert Solution().isPossibleToRearrange(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", t = "zzyyxxwwvvuuttsrrqppoonnmlllkkjjiihhggffeeeddccbbaa", k = 26) == False

assert Solution().isPossibleToRearrange(s = "aaaaaaaaaaaaaa", t = "aaaaaaaaaaaaaa", k = 1) == True

assert Solution().isPossibleToRearrange(s = "qqqqwwwweeeerrrrtttt", t = "wqwqwqwqeertreerttrttt", k = 5) == False

assert Solution().isPossibleToRearrange(s = "mississippiissippiissippiissippiississippiississippiississippiississippi", t = "ppipipipipipipipipipipipipipipipipipipipipipipipippipi", k = 13) == False

assert Solution().isPossibleToRearrange(s = "abcdefghij", t = "jihgfedcba", k = 10) == True

assert Solution().isPossibleToRearrange(s = "aabbccddeeff", t = "ffeeddccbaab", k = 6) == False

assert Solution().isPossibleToRearrange(s = "onetwothreefourfivesixseveneightnineten", t = "eninetonwotwothreefourfivesixseveneightne", k = 5) == False

assert Solution().isPossibleToRearrange(s = "abcdefghabcdefghabcdefgh", t = "abcabcabcdeedefefefgfgfg", k = 9) == False

assert Solution().isPossibleToRearrange(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", t = "zzyyxxwwvvuuttssrrqqppoonnmmllkkjjiihhggffeeeeddccbbaa", k = 26) == False

assert Solution().isPossibleToRearrange(s = "abcdefghijklmnopqrstuvwxyza", t = "zyxwvutsrqponmlkjihgfedcbaa", k = 27) == True

assert Solution().isPossibleToRearrange(s = "abcdefabcdefabcdef", t = "fedcbafedcbafedcba", k = 3) == False

assert Solution().isPossibleToRearrange(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", t = "zzyyxxwwvvuuttrrssqqppoonnllkkjjiihhggffeeddbbaa", k = 26) == False

assert Solution().isPossibleToRearrange(s = "qrstuvqrstuvqrstuv", t = "uuuuvvvvttttssssrrrrqqqqppppooonnnnmmmmllllkkkkjjjjiiiihhhhggggffffeeee", k = 12) == False

assert Solution().isPossibleToRearrange(s = "abcdefghijklmnopqrstuvwxyzaa", t = "zyxwvutsrqponmlkjihgfedcbaaa", k = 27) == True

Answer: assert Solution().isPossibleToRearrange(s = "abcd", t = "cdab", k = 2) == True

Answer: assert Solution().isPossibleToRearrange(s = "abcdefg", t = "gfedcba", k = 1) == False

Answer: assert Solution().isPossibleToRearrange(s = "abcdefg", t = "gfedcba", k = 7) == True

Answer: assert Solution().isPossibleToRearrange(s = "aabbcc", t = "bbaacc", k = 3) == True

Answer: assert Solution().isPossibleToRearrange(s = "abcabcabc", t = "bcbcbcbca", k = 3) == False

Answer: assert Solution().isPossibleToRearrange(s = "aabbcc", t = "bbaacc", k = 2) == False

Answer: assert Solution().isPossibleToRearrange(s = "abacabad", t = "dcabcdab", k = 2) == False

Answer: assert Solution().isPossibleToRearrange(s = "abcdefghijabcdefghijabcdefghij", t = "fedcbafedcbafedcba", k = 3) == False

Answer: assert Solution().isPossibleToRearrange(s = "xyzxyzxyzxyz", t = "zyxzyxzyxzyx", k = 4) == False

Answer: assert Solution().isPossibleToRearrange(s = "xyzyxzyzyzxzyzyz", t = "zyzyzyzyzyzyzyzx", k = 7) == False

Answer: assert Solution().isPossibleToRearrange(s = "abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz", t = "zyxwvutsrqponmlkjihgfedcbazyxwvutsrqponmlkjihgfedcba", k = 26) == False

Answer: assert Solution().isPossibleToRearrange(s = "abcdefghijabcdefghijabcdefghij", t = "abcdefghijabcdefghijabcdefghij", k = 3) == True

Answer: assert Solution().isPossibleToRearrange(s = "abababababab", t = "babababababa", k = 2) == False

Answer: assert Solution().isPossibleToRearrange(s = "aaabbbccc", t = "bbbaaacc", k = 3) == False

Answer: assert Solution().isPossibleToRearrange(s = "mississippiissi", t = "ssissimipissi", k = 5) == False

Answer: assert Solution().isPossibleToRearrange(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", t = "zzzyyxxwwvvuuttssrrqqppoonnmmllkkjjiihhggffeeeeddccbbaa", k = 13) == False

Answer: assert Solution().isPossibleToRearrange(s = "zzyyxxwwvvuuttssrrqqppoonnmmlkkjjiihhaaggeeccbb", t = "bcdeeegghhiikkmnnooppqqrrssttuuvvwwxxyyzz", k = 26) == False

Answer: assert Solution().isPossibleToRearrange(s = "abcdabcdabcdabcdabcdabcd", t = "dddddddcccccbbbbaaaaaa", k = 6) == False

Answer: assert Solution().isPossibleToRearrange(s = "mississippiissim", t = "simississippiiss", k = 6) == False

Answer: assert Solution().isPossibleToRearrange(s = "lkjlkjlkjlkjlkjlkjlkjlkj", t = "llllkkkkjjjjllllkkkkjjjjllllkkkkjjjj", k = 16) == True

Answer: assert Solution().isPossibleToRearrange(s = "aaaaaaaaaaaaaaaaaaaaaaaaaa", t = "aaaaaaaaaaaaaaaaaaaaaaaaaa", k = 10) == True

Answer: assert Solution().isPossibleToRearrange(s = "mmmmmmmmmmnnnnnnnn", t = "nnnnnnnnnnaaaaaaaaaa", k = 5) == False

Answer: assert Solution().isPossibleToRearrange(s = "abacabadabacabad", t = "badabacabadaba", k = 4) == False

Answer: assert Solution().isPossibleToRearrange(s = "aaabbbcccdddeeefffggghhh", t = "hgggfffeeedddcccbbaaa", k = 3) == False

Answer: assert Solution().isPossibleToRearrange(s = "aabbccddeeffgghhiijjkkllmmpqrs", t = "srqpmlkjihgfedcbazyxwvuts", k = 26) == False

Answer: assert Solution().isPossibleToRearrange(s = "xyzxyzxyzxyzxyzxyz", t = "zyxzyxzyxzyxzyxzyx", k = 6) == False

Answer: assert Solution().isPossibleToRearrange(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", t = "zzzyyxxwwvvuuttrrssqqppoonnmmllkkjjiihhggffeeeeddccbbaa", k = 25) == False

Answer: assert Solution().isPossibleToRearrange(s = "aaaabbbbccccdddd", t = "abcdabcdabcdabcd", k = 4) == False

Answer: assert Solution().isPossibleToRearrange(s = "mnopqrsmnopqrsmnopqrsmnopqrsmnopqrs", t = "smnopqrsmnopqrsmnopqrsmnopqrsmnopqrs", k = 10) == False

Answer: assert Solution().isPossibleToRearrange(s = "aaaabbbbccccdddd", t = "ddddccccbbbbaaaa", k = 4) == True

Answer: assert Solution().isPossibleToRearrange(s = "aabbbccddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqqrrrrssssttttuuuuvvvvwwwwxxxxxyyyyyzzzzz", t = "zzzzzyyyyyxxxxwwwwvvvvuuuuttttsssrrrrqqqqpppooonnnmmmlllkkkjjjiiihhhgggfffdddccbbbaaa", k = 26) == False

Answer: assert Solution().isPossibleToRearrange(s = "aaaabbbbccccddddeeeeffffgggghhhhiiii", t = "ihgfedcbihgfedcbihgfedcbihgfedcb", k = 5) == False

Answer: assert Solution().isPossibleToRearrange(s = "qwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnm", t = "mnbvcxzlkjhgfdsapoiuytrewqmnbvcxzlkjhgfdsapoiuytrew", k = 26) == False

Answer: assert Solution().isPossibleToRearrange(s = "aaaaaaabbbbbbbcccccc", t = "abcabcabcabcabcabcabcabc", k = 12) == True

Answer: assert Solution().isPossibleToRearrange(s = "abcdefghijklmnopqrstuabcdefghijklmnopqrstu", t = "utsrqponmlkjihgfedcbautsrqponmlkjihgfedcba", k = 10) == False

Answer: assert Solution().isPossibleToRearrange(s = "abacabadabacaba", t = "acaabbaadabacba", k = 3) == False

Answer: assert Solution().isPossibleToRearrange(s = "abcdeabcdeabcdeabcdeabcdeabcde", t = "deabcdeabcdeabcdeabcdeabcdeabc", k = 6) == False

Answer: assert Solution().isPossibleToRearrange(s = "abcdefgihjklmnopqrstuvwxyz", t = "zyxwvutsrqponmlkjihgfedcba", k = 26) == True

Answer: assert Solution().isPossibleToRearrange(s = "abcdefghijklmnopqrstuv", t = "ponmlkjihgfedcbazyxwvutsr", k = 10) == False

Answer: assert Solution().isPossibleToRearrange(s = "abcdefghijklmnop", t = "ponmlkjihgfedcba", k = 4) == False

Answer: assert Solution().isPossibleToRearrange(s = "abacabadabacabad", t = "daabcbcadabcadba", k = 4) == False

Answer: assert Solution().isPossibleToRearrange(s = "aabbccddeeff", t = "feeddcbaab", k = 2) == False

Answer: assert Solution().isPossibleToRearrange(s = "aaaabbbbccccddddeeeeffffgggghhhhiiiijjjjkkkkllllmmmmnnnnoooo", t = "ooooooooonnnnnmmmmllllkkkkjjjjiiiijjjjhhhhggggeeegfffeeeeddddddccccbbbbaaaa", k = 4) == False

Answer: assert Solution().isPossibleToRearrange(s = "zzzzzzzzzzzzzzzzzzzz", t = "zzzzzzzzzzzzzzzzzzzz", k = 5) == True

Answer: assert Solution().isPossibleToRearrange(s = "abcabcabcabc", t = "cccbbbaaaabc", k = 3) == False

Answer: assert Solution().isPossibleToRearrange(s = "nnnnoooommmmpppp", t = "nopmnopmnopmno", k = 4) == False

Answer: assert Solution().isPossibleToRearrange(s = "abcdefghijabcdefghij", t = "fedcbafedcbafedcba", k = 10) == False

Answer: assert Solution().isPossibleToRearrange(s = "abcdabcdabcdabcd", t = "ddddccccbbbbaaaa", k = 4) == False

Answer: assert Solution().isPossibleToRearrange(s = "abcabcabcabcabcabcabcabc", t = "cbacbacbacbacbacbacbacbacbacba", k = 4) == False

Answer: assert Solution().isPossibleToRearrange(s = "aaaaabbbbccccc", t = "bbbbbcccccddddd", k = 3) == False

Answer: assert Solution().isPossibleToRearrange(s = "aaaabbbbccccddddeeeeffffgggghhhh", t = "abcdefghabcdefghabcdefghabcdefgh", k = 8) == False

Answer: assert Solution().isPossibleToRearrange(s = "xyzxyzxyzxyz", t = "zyxzyxzyxzyx", k = 3) == False

Answer: assert Solution().isPossibleToRearrange(s = "abcdefabcdefabcdefabcdefabcdefabcdef", t = "fedcbafedcbafedcbafedcbafedcba", k = 18) == False

Answer: assert Solution().isPossibleToRearrange(s = "abcdefghijklmnopqrstuvwxyz", t = "zyxwvutsrqponmlkjihgfedcba", k = 26) == True

Answer: assert Solution().isPossibleToRearrange(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", t = "zzyyxxwwvvuuttrrssqqppoonnmmllkkjjiihhggffeeeeddccbbaa", k = 26) == False

Answer: assert Solution().isPossibleToRearrange(s = "mnopqrstuvwxyzabcdefghijkl", t = "abcdefghijklmnopqrstuvwxyz", k = 13) == True

Answer: assert Solution().isPossibleToRearrange(s = "abcdefghijabcdefghij", t = "jihgfedcbajihgfedcba", k = 10) == False

Answer: assert Solution().isPossibleToRearrange(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", k = 26) == True

Answer: assert Solution().isPossibleToRearrange(s = "mmmmnnnnooooppppqqqqrrrrssssttttuuuuvvvvwwwwxxxx", t = "xxxxxxxxwwwwvvvvuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu", k = 20) == False

Answer: assert Solution().isPossibleToRearrange(s = "abcdefghabcdefghabcdefghabcdefgh", t = "ddddccccbbbbaaaaeeeeffffffff", k = 16) == False

Answer: assert Solution().isPossibleToRearrange(s = "xyxyxyxyxyxy", t = "yxyxyxyxyxyx", k = 3) == False

Answer: assert Solution().isPossibleToRearrange(s = "aaaaaaaaaaabbbbbbbbbbbccccccccccdddddddddd", t = "bbbbbbbbbbbbaaaaaaaaaacccccccdddddddddd", k = 10) == False

Answer: assert Solution().isPossibleToRearrange(s = "aaaaaaaaaabbbbbbbbccccccccdddddddd", t = "ddddddddccccccccbbbbbbbbaaaaaaaa", k = 8) == False

Answer: assert Solution().isPossibleToRearrange(s = "zzzzzzzzzzzzzzzzzzzzzzzz", t = "zzzzzzzzzzzzzzzzzzzzzzzz", k = 1) == True

Answer: assert Solution().isPossibleToRearrange(s = "kkkkkkkkkk", t = "kkkkkkkkkk", k = 5) == True

Answer: assert Solution().isPossibleToRearrange(s = "abcdefabcdefabcdefabcdef", t = "aaaabbbbccccddddeeeeffff", k = 8) == False

Answer: assert Solution().isPossibleToRearrange(s = "abcabcabcabcabcabc", t = "cbaabcabcabcabcabc", k = 4) == False

Answer: assert Solution().isPossibleToRearrange(s = "abababababababababababababababab", t = "babababababababababababababababa", k = 2) == False

Answer: assert Solution().isPossibleToRearrange(s = "abcdefghijabcdefghijabcdefghij", t = "abcabcabcabcabcabcabcabcabcabcdeedefefefefefghighighighi", k = 15) == False

Answer: assert Solution().isPossibleToRearrange(s = "racecaracecaracecar", t = "racecaracecaracecar", k = 3) == True

Answer: assert Solution().isPossibleToRearrange(s = "aabbccddeeffgghhiijjkk", t = "jikkhhggffeeddccbbaa", k = 11) == False

Answer: assert Solution().isPossibleToRearrange(s = "xyzxyzxyzxyzxyzxyzxyzxyz", t = "zyxzyxzyxzyxzyxzyxzyxzyxzyx", k = 3) == False

Answer: assert Solution().isPossibleToRearrange(s = "thisisanexampleofalongstringthatweneedtosplit", t = "stingthatweneedtosplitthisisanexampleofalon", k = 7) == False

Answer: assert Solution().isPossibleToRearrange(s = "repeatthispatternrepeatthispatternrepeatthispattern", t = "ternpatrepeaternpatrepeaternpatrepeaternpat", k = 9) == False

Answer: assert Solution().isPossibleToRearrange(s = "abcdefabcdefabcdefabcdef", t = "fabcdfabcdfabcdfabcd", k = 8) == False

Answer: assert Solution().isPossibleToRearrange(s = "abcdefghijklmnopabcdefghijklmnop", t = "pponmlkjihgfedcbazyxwvutsrqponmlkjihgfedcba", k = 16) == False

Answer: assert Solution().isPossibleToRearrange(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", t = "zzzyyxxwwvvuuttrrssqqppoonnmmllkkjjiihhggffeeeeddccbbaa", k = 13) == False

Answer: assert Solution().isPossibleToRearrange(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", k = 26) == True

Answer: assert Solution().isPossibleToRearrange(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", k = 20) == True

Answer: assert Solution().isPossibleToRearrange(s = "abcdefabcdefabcdefabcdefabcdef", t = "fedcbafedcbafedcbafedcba", k = 5) == False

Answer: assert Solution().isPossibleToRearrange(s = "abacabadabacabad", t = "aabbccdaaabbccda", k = 4) == False

Answer: assert Solution().isPossibleToRearrange(s = "abcabcabcabcabcabc", t = "cabacbacbacbacba", k = 6) == False

Answer: assert Solution().isPossibleToRearrange(s = "nnnnoooommmm", t = "mmmmnnnnoooo", k = 3) == True

Answer: assert Solution().isPossibleToRearrange(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", k = 26) == True

Answer: assert Solution().isPossibleToRearrange(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", t = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", k = 1) == True

Answer: assert Solution().isPossibleToRearrange(s = "aabbaabbaabbaabbaabbaabbaabbaabbaabbaabb", t = "bbaabbaabbaabbaabbaabbaabbaabbaabbaabbaa", k = 10) == False

Answer: assert Solution().isPossibleToRearrange(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", t = "zzyyxxwwvvuuttsrrqppoonnmlllkkjjiihhggffeeeddccbbaa", k = 26) == False

Answer: assert Solution().isPossibleToRearrange(s = "aaaaaaaaaaaaaa", t = "aaaaaaaaaaaaaa", k = 1) == True

Answer: assert Solution().isPossibleToRearrange(s = "qqqqwwwweeeerrrrtttt", t = "wqwqwqwqeertreerttrttt", k = 5) == False

Answer: assert Solution().isPossibleToRearrange(s = "mississippiissippiissippiissippiississippiississippiississippiississippi", t = "ppipipipipipipipipipipipipipipipipipipipipipipipippipi", k = 13) == False

Answer: assert Solution().isPossibleToRearrange(s = "abcdefghij", t = "jihgfedcba", k = 10) == True

Answer: assert Solution().isPossibleToRearrange(s = "aabbccddeeff", t = "ffeeddccbaab", k = 6) == False

Answer: assert Solution().isPossibleToRearrange(s = "onetwothreefourfivesixseveneightnineten", t = "eninetonwotwothreefourfivesixseveneightne", k = 5) == False

Answer: assert Solution().isPossibleToRearrange(s = "abcdefghabcdefghabcdefgh", t = "abcabcabcdeedefefefgfgfg", k = 9) == False

Answer: assert Solution().isPossibleToRearrange(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", t = "zzyyxxwwvvuuttssrrqqppoonnmmllkkjjiihhggffeeeeddccbbaa", k = 26) == False

Answer: assert Solution().isPossibleToRearrange(s = "abcdefghijklmnopqrstuvwxyza", t = "zyxwvutsrqponmlkjihgfedcbaa", k = 27) == True

Answer: assert Solution().isPossibleToRearrange(s = "abcdefabcdefabcdef", t = "fedcbafedcbafedcba", k = 3) == False

Answer: assert Solution().isPossibleToRearrange(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", t = "zzyyxxwwvvuuttrrssqqppoonnllkkjjiihhggffeeddbbaa", k = 26) == False

Answer: assert Solution().isPossibleToRearrange(s = "qrstuvqrstuvqrstuv", t = "uuuuvvvvttttssssrrrrqqqqppppooonnnnmmmmllllkkkkjjjjiiiihhhhggggffffeeee", k = 12) == False

Answer: assert Solution().isPossibleToRearrange(s = "abcdefghijklmnopqrstuvwxyzaa", t = "zyxwvutsrqponmlkjihgfedcbaaa", k = 27) == True

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 isPossibleToRearrange(self, s: str, t: str, k: int) -> bool:
        cnt = Counter()
        n = len(s)
        m = n // k
        for i in range(0, n, m):
            cnt[s[i : i + m]] += 1
            cnt[t[i : i + m]] -= 1
        return all(v == 0 for v in cnt.values())

class Solution:
    def isPossibleToRearrange(self, s: str, t: str, k: int) -> bool:


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. This array contains n elements, where exactly n - 2 elements are special numbers. One of the remaining two elements is the sum of these special numbers, and the other is an outlier.
An outlier is defined as a number that is neither one of the original special numbers nor the element representing the sum of those numbers.
Note that special numbers, the sum element, and the outlier must have distinct indices, but may share the same value.
Return the largest potential outlier in nums.

Example 1:

Input: nums = [2,3,5,10]
Output: 10
Explanation:
The special numbers could be 2 and 3, thus making their sum 5 and the outlier 10.

Example 2:

Input: nums = [-2,-1,-3,-6,4]
Output: 4
Explanation:
The special numbers could be -2, -1, and -3, thus making their sum -6 and the outlier 4.

Example 3:

Input: nums = [1,1,1,1,1,5,5]
Output: 5
Explanation:
The special numbers could be 1, 1, 1, 1, and 1, thus making their sum 5 and the other 5 as the outlier.

Constraints:

3 <= nums.length <= 105
-1000 <= nums[i] <= 1000
The input is generated such that at least one potential outlier exists in nums.

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

SOLUTION:

Question:
PROBLEM:
You are given an integer array nums. This array contains n elements, where exactly n - 2 elements are special numbers. One of the remaining two elements is the sum of these special numbers, and the other is an outlier.
An outlier is defined as a number that is neither one of the original special numbers nor the element representing the sum of those numbers.
Note that special numbers, the sum element, and the outlier must have distinct indices, but may share the same value.
Return the largest potential outlier in nums.

Example 1:

Input: nums = [2,3,5,10]
Output: 10
Explanation:
The special numbers could be 2 and 3, thus making their sum 5 and the outlier 10.

Example 2:

Input: nums = [-2,-1,-3,-6,4]
Output: 4
Explanation:
The special numbers could be -2, -1, and -3, thus making their sum -6 and the outlier 4.

Example 3:

Input: nums = [1,1,1,1,1,5,5]
Output: 5
Explanation:
The special numbers could be 1, 1, 1, 1, and 1, thus making their sum 5 and the other 5 as the outlier.

Constraints:

3 <= nums.length <= 105
-1000 <= nums[i] <= 1000
The input is generated such that at least one potential outlier exists in nums.

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

SOLUTION:

assert Solution().getLargestOutlier(nums = [1000,-1000,0,500,-500]) == 1000

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

assert Solution().getLargestOutlier(nums = [5,5,5,5,5,25,30]) == 30

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

assert Solution().getLargestOutlier(nums = [2,3,5,10]) == 10

assert Solution().getLargestOutlier(nums = [100,200,300,600,500]) == 500

assert Solution().getLargestOutlier(nums = [10,20,30,60,5]) == 5

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

assert Solution().getLargestOutlier(nums = [-5,-5,-10,0,15]) == 15

assert Solution().getLargestOutlier(nums = [-1,-2,-3,-6,10]) == 10

assert Solution().getLargestOutlier(nums = [-2,-1,-3,-6,4]) == 4

assert Solution().getLargestOutlier(nums = [500,500,1000,-500,500]) == 1000

assert Solution().getLargestOutlier(nums = [-1,-2,-3,-4,-5,-6,-15]) == -6

assert Solution().getLargestOutlier(nums = [10,20,30,60,100]) == 100

assert Solution().getLargestOutlier(nums = [3,3,3,3,3,3,9]) == -inf

assert Solution().getLargestOutlier(nums = [5,5,5,5,5,5,5,15]) == -inf

assert Solution().getLargestOutlier(nums = [-5,-5,-5,-5,-5,-10,40]) == -inf

assert Solution().getLargestOutlier(nums = [1000,-1000,0,1000]) == 1000

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

assert Solution().getLargestOutlier(nums = [-10, -20, -30, -60, 10, 100, 101]) == -inf

assert Solution().getLargestOutlier(nums = [-1, -2, -3, -6, -10, -20, -30]) == -inf

assert Solution().getLargestOutlier(nums = [-1, -2, -3, -4, -5, -6, -15, -20]) == -inf

assert Solution().getLargestOutlier(nums = [1, 1, 1, 1, 1, 5, 5, 5, 5, 5]) == -inf

assert Solution().getLargestOutlier(nums = [1, 1, 2, 2, 3, 3, 5, 5, 8, 8, 13, 21]) == -inf

assert Solution().getLargestOutlier(nums = [1, 2, 3, 4, 5, 6, 10, 15]) == -inf

assert Solution().getLargestOutlier(nums = [3, 3, 3, 3, 3, 3, 3, 21, 9]) == 9

assert Solution().getLargestOutlier(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 12]) == -inf

assert Solution().getLargestOutlier(nums = [10, 20, 30, 60, 100, 200, 300]) == -inf

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

assert Solution().getLargestOutlier(nums = [50, 50, 50, 150, 150, 250, 300]) == -inf

assert Solution().getLargestOutlier(nums = [-1, -2, -3, -6, 1, -100, 100]) == 1

assert Solution().getLargestOutlier(nums = [10, 20, 30, 60, 100, 200, 300, 600]) == -inf

assert Solution().getLargestOutlier(nums = [999, 1, 1000, 1001, 2, 1002]) == -inf

assert Solution().getLargestOutlier(nums = [0, 0, 0, 0, 0, 5, 5]) == 0

assert Solution().getLargestOutlier(nums = [5, 10, 15, 30, 45, 50, 100]) == -inf

assert Solution().getLargestOutlier(nums = [1, 2, 3, 4, 5, 6, 10, 21]) == 10

assert Solution().getLargestOutlier(nums = [1, 2, 3, 4, 5, 15, 16]) == 16

assert Solution().getLargestOutlier(nums = [100, 200, 300, 600, 700, 800, 900]) == -inf

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

assert Solution().getLargestOutlier(nums = [10, 20, 30, 60, 50, 100, 70]) == -inf

assert Solution().getLargestOutlier(nums = [100, 200, 300, 600, 1000]) == 1000

assert Solution().getLargestOutlier(nums = [100, 200, 300, 600, 1000, 1500]) == -inf

assert Solution().getLargestOutlier(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]) == -1

assert Solution().getLargestOutlier(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 55]) == -inf

assert Solution().getLargestOutlier(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 9]) == -inf

assert Solution().getLargestOutlier(nums = [1, 2, 3, 6, 10, 20, 30]) == -inf

assert Solution().getLargestOutlier(nums = [10, 20, 30, 40, 50, 60, 150, 1000]) == -inf

assert Solution().getLargestOutlier(nums = [1, 2, 3, 6, 10, 11, 12, 13, 14, 15]) == -inf

assert Solution().getLargestOutlier(nums = [50, 50, 50, 50, 50, 250, 251]) == 251

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

Answer: assert Solution().getLargestOutlier(nums = [1000,-1000,0,500,-500]) == 1000

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

Answer: assert Solution().getLargestOutlier(nums = [5,5,5,5,5,25,30]) == 30

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

Answer: assert Solution().getLargestOutlier(nums = [-999,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1000]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [2,3,5,10]) == 10

Answer: assert Solution().getLargestOutlier(nums = [100,200,300,600,500]) == 500

Answer: assert Solution().getLargestOutlier(nums = [10,20,30,60,5]) == 5

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

Answer: assert Solution().getLargestOutlier(nums = [1000,-1000,0,1000,-1000,0]) == 0

Answer: assert Solution().getLargestOutlier(nums = [-5,-5,-10,0,15]) == 15

Answer: assert Solution().getLargestOutlier(nums = [-1,-2,-3,-6,10]) == 10

Answer: assert Solution().getLargestOutlier(nums = [1000, -1000, 0, 1999, 2000]) == 1999

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

Answer: assert Solution().getLargestOutlier(nums = [500,500,1000,-500,500]) == 1000

Answer: assert Solution().getLargestOutlier(nums = [999,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [-1,-2,-3,-4,-5,-6,-15]) == -6

Answer: assert Solution().getLargestOutlier(nums = [10,20,30,60,100]) == 100

Answer: assert Solution().getLargestOutlier(nums = [3,3,3,3,3,3,9]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [5,5,5,5,5,5,5,15]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [-5,-5,-5,-5,-5,-10,40]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [1000,-1000,0,1000]) == 1000

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

Answer: assert Solution().getLargestOutlier(nums = [-10, -20, -30, -60, 10, 100, 101]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [10, -10, 20, -20, 30, -30, 40, -40, 50, -50, 100, -100, 150, -150, 200, -200, 250, -250, 300, -300, 350]) == 250

Answer: assert Solution().getLargestOutlier(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 45, 55]) == 45

Answer: assert Solution().getLargestOutlier(nums = [100, 200, 300, 600, 400, 500, 700, 800, 900, 1000, 1500]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [-1, -2, -3, -6, -10, -20, -30]) == -inf

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

Answer: assert Solution().getLargestOutlier(nums = [-100, -200, -300, -600, 10, 20, 30, 40, 50]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [-1, -2, -3, -4, -5, -6, -15, -20]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [1, 1, 1, 1, 1, 5, 5, 5, 5, 5]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [100, 100, 100, 300, 400, 500, 600, 700]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [1000, -1000, 0, 0, 0, 1999, 2000, 3000]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [1, 1, 2, 2, 3, 3, 5, 5, 8, 8, 13, 21]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [999, 1, 1000, 1999, 500, 500, 1500]) == -inf

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

Answer: assert Solution().getLargestOutlier(nums = [100, 200, 300, 400, 500, 1500, 1501]) == 1501

Answer: assert Solution().getLargestOutlier(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 55, 100]) == 100

Answer: assert Solution().getLargestOutlier(nums = [1, 2, 3, 4, 5, 6, 10, 15]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [3, 3, 3, 3, 3, 3, 3, 21, 9]) == 9

Answer: assert Solution().getLargestOutlier(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20, -210]) == -inf

Answer: assert Solution().getLargestOutlier(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, 50]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [-100, -200, -300, -600, -700, -800, -900]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [-1000, 1000, 0, 0, 0, -1999, -2000, -3000]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 12]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [-100, -200, -300, -600, -400, -500, -700, -800]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 3500]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [-100, -200, -300, -400, -500, -1500, 1500]) == 1500

Answer: assert Solution().getLargestOutlier(nums = [10, 20, 30, 60, 100, 200, 300]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 210]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [100, 200, 300, 600, 400, 500, 700, 800]) == -inf

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

Answer: assert Solution().getLargestOutlier(nums = [-1000, -1000, -1000, -1000, -1000, -1000, -1000, -1000, -1000, -1000, -10000]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 550]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000]) == 1000

Answer: assert Solution().getLargestOutlier(nums = [50, 50, 50, 150, 150, 250, 300]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [1000, -500, 500, 0, 2000, 3000, 4000]) == 4000

Answer: assert Solution().getLargestOutlier(nums = [-1, -2, -3, -6, 1, -100, 100]) == 1

Answer: assert Solution().getLargestOutlier(nums = [1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0

Answer: assert Solution().getLargestOutlier(nums = [10, 20, 30, 60, 100, 200, 300, 600]) == -inf

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

Answer: assert Solution().getLargestOutlier(nums = [500, 500, 1000, 1001, 999, 998, 997]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [999, 1, 1000, 1001, 2, 1002]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [500, 500, 500, 500, 500, 2500, 3000]) == 3000

Answer: assert Solution().getLargestOutlier(nums = [0, 0, 0, 0, 0, 5, 5]) == 0

Answer: assert Solution().getLargestOutlier(nums = [5, 10, 15, 30, 45, 50, 100]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [-500, -500, -500, -500, -500, -2500, -3000]) == -3000

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

Answer: assert Solution().getLargestOutlier(nums = [1, 2, 3, 4, 5, 6, 10, 21]) == 10

Answer: assert Solution().getLargestOutlier(nums = [1000, 2000, 3000, 6000, 10000, 15000, 20000]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 20]) == -inf

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

Answer: assert Solution().getLargestOutlier(nums = [100, 200, 300, 500, 1000, 1500, 2000, 2500, 3000, 3500]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -55]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [1, 2, 3, 4, 5, 15, 16]) == 16

Answer: assert Solution().getLargestOutlier(nums = [-1, -2, -3, -4, -5, -10, -15, 20]) == -10

Answer: assert Solution().getLargestOutlier(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 1000]) == 1000

Answer: assert Solution().getLargestOutlier(nums = [1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 10000]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [-100, -200, -300, -600, -1000, -1500, 2000]) == -1500

Answer: assert Solution().getLargestOutlier(nums = [100, 200, 300, 600, 700, 800, 900]) == -inf

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

Answer: assert Solution().getLargestOutlier(nums = [-100, -100, -200, -300, -400, -500, -600, -700]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [500, -500, 0, 1000, -1000, 1500, -2000, 3000]) == 1500

Answer: assert Solution().getLargestOutlier(nums = [1, 2, 3, 6, 9, 12, 15, 18, 21, 24, 100]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [10, 20, 30, 60, 50, 100, 70]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [-100, -200, -300, -500, -1000, -1500, -2000, -2500, -3000, -3500]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [-1, -1, -2, -2, -3, -3, -5, -5, -8, -8, -13, -21, 34]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [100, 200, 300, 600, 1000]) == 1000

Answer: assert Solution().getLargestOutlier(nums = [100, 101, 102, 303, 404, 505, 606, 707, 808, 909, 1010]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [100, 200, 300, 600, 1000, 1500]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]) == -1

Answer: assert Solution().getLargestOutlier(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 100]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [-1, -1, -1, -1, -1, -1, -1, -1, -1, -9]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [-100, -200, -300, -400, -500, -600, -700, -800, -900, -1000, -5500, -6500, 7500]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 5500, 6500]) == 6500

Answer: assert Solution().getLargestOutlier(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 55]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [-10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -100]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [999, -999, 0, 0, 0, 1998, 2000]) == 2000

Answer: assert Solution().getLargestOutlier(nums = [-10, -20, -30, -40, -50, -60, -150, -1000]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 9]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [100, 200, 300, 600, 1200, 2400, 4800]) == 4800

Answer: assert Solution().getLargestOutlier(nums = [-300, -200, -500, -1000, -1500, 500]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [-1, -2, -3, -4, -5, -6, -10, -21]) == -10

Answer: assert Solution().getLargestOutlier(nums = [-1000, -1000, -1000, -3000, 500, 600, 700, 800, 900]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [500, 500, 1000, 1001, 250, 250, 1500]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, -1000, -2000, -3000]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [1, 2, 3, 6, 10, 20, 30]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [-1, -2, -3, -6, -9, -12, -15, -18, -21, -24, -100]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [10, 20, 30, 60, 40, 50, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [10, 20, 30, 40, 50, 60, 150, 1000]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [1, 2, 3, 6, 10, 11, 12, 13, 14, 15]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [-100, -200, -300, -600, 100, 200, 300]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [100, 200, 300, 400, 500, 600, 1500, 1600, 1700]) == -inf

Answer: assert Solution().getLargestOutlier(nums = [50, 50, 50, 50, 50, 250, 251]) == 251

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

Answer: assert Solution().getLargestOutlier(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000]) == 1000

Answer: assert Solution().getLargestOutlier(nums = [999, 999, 999, 999, 999, 4995, 5000]) == 5000

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 getLargestOutlier(self, nums: List[int]) -> int:
        s = sum(nums)
        cnt = Counter(nums)
        ans = -inf
        for x, v in cnt.items():
            t = s - x
            if t % 2 or cnt[t // 2] == 0:
                continue
            if x != t // 2 or v > 1:
                ans = max(ans, 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 an array points where points[i] = [xi, yi] represents the coordinates of a point on an infinite plane.
Your task is to find the maximum area of a rectangle that:

Can be formed using four of these points as its corners.
Does not contain any other point inside or on its border.
Has its edges parallel to the axes.

Return the maximum area that you can obtain or -1 if no such rectangle is possible.

Example 1:

Input: points = [[1,1],[1,3],[3,1],[3,3]]
Output: 4
Explanation:

We can make a rectangle with these 4 points as corners and there is no other point that lies inside or on the border. Hence, the maximum possible area would be 4.

Example 2:

Input: points = [[1,1],[1,3],[3,1],[3,3],[2,2]]
Output: -1
Explanation:

There is only one rectangle possible is with points [1,1], [1,3], [3,1] and [3,3] but [2,2] will always lie inside it. Hence, returning -1.

Example 3:

Input: points = [[1,1],[1,3],[3,1],[3,3],[1,2],[3,2]]
Output: 2
Explanation:

The maximum area rectangle is formed by the points [1,3], [1,2], [3,2], [3,3], which has an area of 2. Additionally, the points [1,1], [1,2], [3,1], [3,2] also form a valid rectangle with the same area.

Constraints:

1 <= points.length <= 10
points[i].length == 2
0 <= xi, yi <= 100
All the given points are unique.

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

SOLUTION:

Question:
PROBLEM:
You are given an array points where points[i] = [xi, yi] represents the coordinates of a point on an infinite plane.
Your task is to find the maximum area of a rectangle that:

Can be formed using four of these points as its corners.
Does not contain any other point inside or on its border.
Has its edges parallel to the axes.

Return the maximum area that you can obtain or -1 if no such rectangle is possible.

Example 1:

Input: points = [[1,1],[1,3],[3,1],[3,3]]
Output: 4
Explanation:

We can make a rectangle with these 4 points as corners and there is no other point that lies inside or on the border. Hence, the maximum possible area would be 4.

Example 2:

Input: points = [[1,1],[1,3],[3,1],[3,3],[2,2]]
Output: -1
Explanation:

There is only one rectangle possible is with points [1,1], [1,3], [3,1] and [3,3] but [2,2] will always lie inside it. Hence, returning -1.

Example 3:

Input: points = [[1,1],[1,3],[3,1],[3,3],[1,2],[3,2]]
Output: 2
Explanation:

The maximum area rectangle is formed by the points [1,3], [1,2], [3,2], [3,3], which has an area of 2. Additionally, the points [1,1], [1,2], [3,1], [3,2] also form a valid rectangle with the same area.

Constraints:

1 <= points.length <= 10
points[i].length == 2
0 <= xi, yi <= 100
All the given points are unique.

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

SOLUTION:

assert Solution().maxRectangleArea(points = [[0,0],[0,1],[1,0],[1,1]]) == 1

assert Solution().maxRectangleArea(points = [[1,1],[2,2],[3,3]]) == -1

assert Solution().maxRectangleArea(points = [[5,5],[5,7],[7,5],[7,7]]) == 4

assert Solution().maxRectangleArea(points = [[0,0],[1,0],[0,1],[1,1]]) == 1

assert Solution().maxRectangleArea(points = [[1,1],[2,2],[3,3],[4,4]]) == -1

assert Solution().maxRectangleArea(points = [[0,0],[100,100]]) == -1

assert Solution().maxRectangleArea(points = [[1,1],[1,3],[3,1],[3,3]]) == 4

Answer: assert Solution().maxRectangleArea(points = [[0,0],[0,1],[1,0],[1,1],[2,2],[2,3],[3,2],[3,3]]) == 1

Answer: assert Solution().maxRectangleArea(points = [[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[0,2],[1,2],[2,2]]) == 1

Answer: assert Solution().maxRectangleArea(points = [[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[3,1],[3,2],[3,3]]) == 1

Answer: assert Solution().maxRectangleArea(points = [[0,0],[0,1],[1,0],[1,1]]) == 1

Answer: assert Solution().maxRectangleArea(points = [[1,1],[1,3],[3,1],[3,3],[1,2],[3,2]]) == 2

Answer: assert Solution().maxRectangleArea(points = [[1,1],[1,3],[3,1],[3,3],[2,2]]) == -1

Answer: assert Solution().maxRectangleArea(points = [[10,10],[10,20],[20,10],[20,20],[15,15]]) == -1

Answer: assert Solution().maxRectangleArea(points = [[1,1],[2,2],[3,3]]) == -1

Answer: assert Solution().maxRectangleArea(points = [[5,5],[5,7],[7,5],[7,7]]) == 4

Answer: assert Solution().maxRectangleArea(points = [[10,10],[10,20],[20,10],[20,20]]) == 100

Answer: assert Solution().maxRectangleArea(points = [[0,0],[1,0],[0,1],[1,1],[2,0],[2,1],[0,2],[1,2],[2,2]]) == 1

Answer: assert Solution().maxRectangleArea(points = [[0,0],[0,3],[3,0],[3,3],[1,1],[2,2]]) == -1

Answer: assert Solution().maxRectangleArea(points = [[0,0],[1,0],[2,0],[0,1],[1,1],[2,1]]) == 1

Answer: assert Solution().maxRectangleArea(points = [[0,0],[1,0],[0,1],[1,1]]) == 1

Answer: assert Solution().maxRectangleArea(points = [[5,5],[5,6],[6,5],[6,6],[7,7],[7,8],[8,7],[8,8]]) == 1

Answer: assert Solution().maxRectangleArea(points = [[0,0],[0,2],[2,0],[2,2],[1,1]]) == -1

Answer: assert Solution().maxRectangleArea(points = [[1,1],[1,2],[2,1],[2,2],[3,3],[3,4],[4,3],[4,4]]) == 1

Answer: assert Solution().maxRectangleArea(points = [[1,1],[2,2],[3,3],[4,4]]) == -1

Answer: assert Solution().maxRectangleArea(points = [[0,0],[100,100]]) == -1

Answer: assert Solution().maxRectangleArea(points = [[1,1],[1,3],[3,1],[3,3]]) == 4

Answer: assert Solution().maxRectangleArea(points = [[0,0],[0,1],[1,0],[1,1],[2,2]]) == 1

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

Answer: assert Solution().maxRectangleArea(points = [[0,0],[0,10],[10,0],[10,10],[5,5],[5,6],[6,5],[6,6],[1,9],[9,1],[9,9]]) == 1

Answer: assert Solution().maxRectangleArea(points = [[0,0],[0,10],[10,0],[10,10],[2,2],[2,8],[8,2],[8,8],[5,5],[5,0],[0,5],[10,5],[5,10]]) == -1

Answer: assert Solution().maxRectangleArea(points = [[1,1],[1,4],[4,1],[4,4],[2,2],[3,2],[2,3],[3,3],[1,2],[2,1],[3,1],[4,2]]) == 1

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

Answer: assert Solution().maxRectangleArea(points = [[1,1],[1,4],[4,1],[4,4],[2,2],[2,3],[3,2],[3,3]]) == 1

Answer: assert Solution().maxRectangleArea(points = [[1,1],[1,5],[5,1],[5,5],[3,3],[4,4],[2,2]]) == -1

Answer: assert Solution().maxRectangleArea(points = [[2,3],[2,5],[3,2],[3,5],[3,8],[5,2],[5,3],[5,8],[8,2],[8,3],[8,5]]) == 3

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

Answer: assert Solution().maxRectangleArea(points = [[10,10],[10,20],[20,10],[20,20],[15,15],[12,12],[18,18]]) == -1

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

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

Answer: assert Solution().maxRectangleArea(points = [[1,1],[1,7],[7,1],[7,7],[2,2],[2,6],[6,2],[6,6],[3,3],[3,5],[5,3],[5,5],[4,4],[4,6],[6,4]]) == -1

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

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

Answer: assert Solution().maxRectangleArea(points = [[1,1],[1,4],[4,1],[4,4],[2,2],[3,3],[2,3],[3,2]]) == 1

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

Answer: assert Solution().maxRectangleArea(points = [[1,2],[1,4],[2,1],[2,5],[4,2],[4,4],[5,1],[5,5],[3,3]]) == -1

Answer: assert Solution().maxRectangleArea(points = [[1,1],[1,4],[4,1],[4,4],[2,2],[3,3],[1,2],[2,1],[3,4],[4,3]]) == 1

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

Answer: assert Solution().maxRectangleArea(points = [[0,0],[0,3],[3,0],[3,3],[1,1],[1,2],[2,1],[2,2],[1,0],[0,1],[3,1],[1,3],[0,2],[2,0],[2,3],[3,2]]) == 1

Answer: assert Solution().maxRectangleArea(points = [[1,1],[1,7],[7,1],[7,7],[2,2],[2,6],[6,2],[6,6],[3,3],[3,5],[5,3],[5,5],[4,4]]) == -1

Answer: assert Solution().maxRectangleArea(points = [[10,10],[10,15],[15,10],[15,15],[12,12],[12,13],[13,12],[13,13],[11,11],[11,14],[14,11],[14,14]]) == 1

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

Answer: assert Solution().maxRectangleArea(points = [[0,0],[1,0],[2,0],[3,0],[0,1],[1,1],[2,1],[3,1],[0,2],[1,2],[2,2],[3,2]]) == 1

Answer: assert Solution().maxRectangleArea(points = [[0,0],[1,0],[2,0],[0,2],[1,2],[2,2],[1,1],[2,1],[0,1]]) == 1

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

Answer: assert Solution().maxRectangleArea(points = [[0,0],[0,3],[0,6],[1,1],[1,4],[1,7],[2,2],[2,5],[3,0],[3,3],[3,6],[4,1],[4,4],[4,7],[5,2],[5,5],[6,0],[6,3],[6,6],[7,1],[7,4],[7,7]]) == -1

Answer: assert Solution().maxRectangleArea(points = [[0,0],[1,0],[2,0],[0,1],[1,1],[2,1],[0,2],[1,2],[2,2],[3,3]]) == 1

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

Answer: assert Solution().maxRectangleArea(points = [[0,0],[0,10],[10,0],[10,10],[2,2],[2,8],[8,2],[8,8],[5,5]]) == -1

Answer: assert Solution().maxRectangleArea(points = [[10,10],[10,20],[20,10],[20,20],[15,15],[15,25],[25,15],[25,25],[15,10],[10,15]]) == 25

Answer: assert Solution().maxRectangleArea(points = [[1,1],[1,6],[6,1],[6,6],[2,2],[2,4],[4,2],[4,4],[3,3],[3,5],[5,3],[5,5]]) == -1

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

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

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

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

Answer: assert Solution().maxRectangleArea(points = [[1,1],[1,5],[5,1],[5,5],[2,2],[2,3],[2,4],[3,2],[3,4],[4,2],[4,3],[4,4]]) == -1

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

Answer: assert Solution().maxRectangleArea(points = [[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[3,1],[3,2],[3,3],[2,4],[4,2],[4,4]]) == 1

Answer: assert Solution().maxRectangleArea(points = [[1,1],[1,2],[2,1],[2,2],[3,3],[3,4],[4,3],[4,4],[2,3],[3,2]]) == 1

Answer: assert Solution().maxRectangleArea(points = [[10,10],[10,20],[20,10],[20,20],[15,15],[5,5],[25,25]]) == -1

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

Answer: assert Solution().maxRectangleArea(points = [[0,0],[1,0],[2,0],[3,0],[0,1],[1,1],[2,1],[3,1],[0,2],[1,2],[2,2],[3,2],[0,3],[1,3],[2,3],[3,3]]) == 1

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

Answer: assert Solution().maxRectangleArea(points = [[1,1],[1,2],[2,1],[2,2],[1,3],[2,3],[3,1],[3,2],[3,3],[4,1],[4,2],[4,3],[1,4],[2,4],[3,4],[4,4]]) == 1

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

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

Answer: assert Solution().maxRectangleArea(points = [[0,0],[0,9],[9,0],[9,9],[3,3],[3,6],[6,3],[6,6],[1,1],[1,8],[8,1],[8,8]]) == 9

Answer: assert Solution().maxRectangleArea(points = [[0,0],[0,2],[2,0],[2,2],[1,1],[1,3],[3,1],[3,3],[1,2],[2,1],[2,3],[3,2]]) == 1

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

Answer: assert Solution().maxRectangleArea(points = [[1,1],[1,5],[5,1],[5,5],[2,2],[2,3],[3,2],[3,4],[4,3],[4,4]]) == -1

Answer: assert Solution().maxRectangleArea(points = [[0,0],[10,0],[0,10],[10,10],[5,5],[5,0],[0,5],[10,5],[5,10]]) == 25

Answer: assert Solution().maxRectangleArea(points = [[0,0],[0,10],[5,0],[5,10],[10,0],[10,10],[2,2],[2,8],[8,2],[8,8]]) == 36

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

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

Answer: assert Solution().maxRectangleArea(points = [[1,5],[1,10],[5,1],[5,10],[10,1],[10,5],[2,2],[8,8],[3,3],[7,7]]) == -1

Answer: assert Solution().maxRectangleArea(points = [[5,5],[5,8],[8,5],[8,8],[6,6],[6,7],[7,6],[7,7],[9,9],[9,10],[10,9],[10,10],[1,1],[1,2],[2,1],[2,2]]) == 1

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

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

Answer: assert Solution().maxRectangleArea(points = [[0,0],[0,2],[2,0],[2,2],[1,1],[1,3],[3,1],[3,3]]) == -1

Answer: assert Solution().maxRectangleArea(points = [[1,1],[1,6],[6,1],[6,6],[2,3],[2,5],[3,2],[3,4],[4,3],[4,5],[5,2],[5,4]]) == -1

Answer: assert Solution().maxRectangleArea(points = [[10,10],[10,15],[10,20],[15,10],[15,15],[15,20],[20,10],[20,15],[20,20],[25,25],[25,30],[30,25],[30,30]]) == 25

Answer: assert Solution().maxRectangleArea(points = [[0,0],[0,1],[1,0],[1,1],[2,2],[2,3],[3,2],[3,3],[0,3],[3,0],[1,2],[2,1]]) == 1

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

Answer: assert Solution().maxRectangleArea(points = [[0,0],[0,3],[3,0],[3,3],[1,1],[1,2],[2,1],[2,2],[1,3],[3,1],[2,3],[3,2],[1,0],[0,1],[2,0],[0,2]]) == 1

Answer: assert Solution().maxRectangleArea(points = [[1,1],[1,4],[4,1],[4,4],[2,2],[2,3],[3,2],[3,3],[1,3],[3,1],[2,1],[4,2]]) == 1

Answer: assert Solution().maxRectangleArea(points = [[1,1],[1,4],[4,1],[4,4],[2,2],[3,3],[5,5]]) == -1

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

Answer: assert Solution().maxRectangleArea(points = [[1,1],[1,5],[2,2],[2,4],[3,3],[4,1],[4,5],[5,2],[5,4]]) == -1

Answer: assert Solution().maxRectangleArea(points = [[10,10],[10,20],[20,10],[20,20],[15,15],[15,25],[25,15],[25,25],[10,15],[15,10]]) == 25

Answer: assert Solution().maxRectangleArea(points = [[1,1],[1,5],[5,1],[5,5],[2,2],[3,3],[4,4],[6,6],[7,7],[8,8]]) == -1

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

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

inf = float('inf')

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

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

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

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

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

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

class Solution:
    def maxRectangleArea(self, points: List[List[int]]) -> int:
        def check(x1: int, y1: int, x2: int, y2: int) -> bool:
            cnt = 0
            for x, y in points:
                if x < x1 or x > x2 or y < y1 or y > y2:
                    continue
                if (x == x1 or x == x2) and (y == y1 or y == y2):
                    cnt += 1
                    continue
                return False
            return cnt == 4

        ans = -1
        for i, (x1, y1) in enumerate(points):
            for x2, y2 in points[:i]:
                x3, y3 = min(x1, x2), min(y1, y2)
                x4, y4 = max(x1, x2), max(y1, y2)
                if check(x3, y3, x4, y4):
                    ans = max(ans, (x4 - x3) * (y4 - y3))
        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 array of integers nums and an integer k.
Return the maximum sum of a subarray of nums, such that the size of the subarray is divisible by k.

Example 1:

Input: nums = [1,2], k = 1
Output: 3
Explanation:
The subarray [1, 2] with sum 3 has length equal to 2 which is divisible by 1.

Example 2:

Input: nums = [-1,-2,-3,-4,-5], k = 4
Output: -10
Explanation:
The maximum sum subarray is [-1, -2, -3, -4] which has length equal to 4 which is divisible by 4.

Example 3:

Input: nums = [-5,1,2,-3,4], k = 2
Output: 4
Explanation:
The maximum sum subarray is [1, 2, -3, 4] which has length equal to 4 which is divisible by 2.

Constraints:

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

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

SOLUTION:

Question:
PROBLEM:
You are given an array of integers nums and an integer k.
Return the maximum sum of a subarray of nums, such that the size of the subarray is divisible by k.

Example 1:

Input: nums = [1,2], k = 1
Output: 3
Explanation:
The subarray [1, 2] with sum 3 has length equal to 2 which is divisible by 1.

Example 2:

Input: nums = [-1,-2,-3,-4,-5], k = 4
Output: -10
Explanation:
The maximum sum subarray is [-1, -2, -3, -4] which has length equal to 4 which is divisible by 4.

Example 3:

Input: nums = [-5,1,2,-3,4], k = 2
Output: 4
Explanation:
The maximum sum subarray is [1, 2, -3, 4] which has length equal to 4 which is divisible by 2.

Constraints:

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

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

SOLUTION:

assert Solution().maxSubarraySum(nums = [10,20,30,40,50,60], k = 5) == 200

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

assert Solution().maxSubarraySum(nums = [0,0,0,0,0,0,0,0,0,0], k = 5) == 0

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

assert Solution().maxSubarraySum(nums = [0,0,0,0,0], k = 2) == 0

assert Solution().maxSubarraySum(nums = [-1,-2,-3,-4,-5], k = 4) == -10

assert Solution().maxSubarraySum(nums = [3,2,1,4,5], k = 3) == 10

assert Solution().maxSubarraySum(nums = [10,20,30,40,50], k = 5) == 150

assert Solution().maxSubarraySum(nums = [5,5,5,5,5,5], k = 2) == 30

assert Solution().maxSubarraySum(nums = [0,0,0,0,0,0,0,0,0,0], k = 1) == 0

assert Solution().maxSubarraySum(nums = [3,5,6,7,8,9], k = 3) == 38

assert Solution().maxSubarraySum(nums = [5,5,5,5,5,5,5,5], k = 3) == 30

assert Solution().maxSubarraySum(nums = [0,0,0,0,0], k = 3) == 0

assert Solution().maxSubarraySum(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], k = 1) == 0

assert Solution().maxSubarraySum(nums = [3, 5, 7, 2, 8, 6, 4, 1, 9], k = 3) == 45

assert Solution().maxSubarraySum(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], k = 5) == 0

assert Solution().maxSubarraySum(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], k = 4) == 8

Answer: assert Solution().maxSubarraySum(nums = [1000000000,-1000000000,1000000000,-1000000000,1000000000], k = 2) == 0

Answer: assert Solution().maxSubarraySum(nums = [1000000000,-1000000000,1000000000,-1000000000], k = 2) == 0

Answer: assert Solution().maxSubarraySum(nums = [1,2,3,4,5,6,7,8,9,10], k = 10) == 55

Answer: assert Solution().maxSubarraySum(nums = [1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000], k = 10) == 10000000000

Answer: assert Solution().maxSubarraySum(nums = [10,20,30,40,50,60], k = 5) == 200

Answer: assert Solution().maxSubarraySum(nums = [-1000000000,-1000000000,-1000000000,-1000000000], k = 3) == -3000000000

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

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

Answer: assert Solution().maxSubarraySum(nums = [0,0,0,0,0,0,0,0,0,0], k = 5) == 0

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

Answer: assert Solution().maxSubarraySum(nums = [1000000000,1000000000,1000000000,1000000000], k = 2) == 4000000000

Answer: assert Solution().maxSubarraySum(nums = [1,-1,1,-1,1,-1,1,-1,1,-1], k = 2) == 0

Answer: assert Solution().maxSubarraySum(nums = [0,0,0,0,0], k = 2) == 0

Answer: assert Solution().maxSubarraySum(nums = [1,2,3,4,5,6,7,8,9,10], k = 5) == 55

Answer: assert Solution().maxSubarraySum(nums = [-1,-2,-3,-4,-5], k = 4) == -10

Answer: assert Solution().maxSubarraySum(nums = [1,1,1,1,1,1,1,1,1,1], k = 5) == 10

Answer: assert Solution().maxSubarraySum(nums = [3,2,1,4,5], k = 3) == 10

Answer: assert Solution().maxSubarraySum(nums = [10,20,30,40,50], k = 5) == 150

Answer: assert Solution().maxSubarraySum(nums = [-10,-20,-30,-40,-50], k = 2) == -30

Answer: assert Solution().maxSubarraySum(nums = [-10,-20,-30,-40,-50,-60,-70,-80,-90,-100], k = 3) == -60

Answer: assert Solution().maxSubarraySum(nums = [2,2,2,2,2,2,2,2,2,2], k = 3) == 18

Answer: assert Solution().maxSubarraySum(nums = [5,5,5,5,5,5], k = 2) == 30

Answer: assert Solution().maxSubarraySum(nums = [0,0,0,0,0,0,0,0,0,0], k = 1) == 0

Answer: assert Solution().maxSubarraySum(nums = [-10,-20,-30,-40,-50,-60,-70,-80,-90,-100], k = 5) == -150

Answer: assert Solution().maxSubarraySum(nums = [10,20,30,40,50,60,70,80,90,100], k = 10) == 550

Answer: assert Solution().maxSubarraySum(nums = [1,-1,1,-1,1,-1,1,-1,1,-1], k = 5) == 1

Answer: assert Solution().maxSubarraySum(nums = [3,5,6,7,8,9], k = 3) == 38

Answer: assert Solution().maxSubarraySum(nums = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20], k = 5) == 210

Answer: assert Solution().maxSubarraySum(nums = [1000000000,1000000000,1000000000,1000000000,1000000000], k = 5) == 5000000000

Answer: assert Solution().maxSubarraySum(nums = [5,5,5,5,5,5,5,5], k = 3) == 30

Answer: assert Solution().maxSubarraySum(nums = [0,0,0,0,0], k = 3) == 0

Answer: assert Solution().maxSubarraySum(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], k = 10) == 310

Answer: assert Solution().maxSubarraySum(nums = [3, -1, 4, 1, -5, 9, 2, -6, 5, -3], k = 3) == 12

Answer: assert Solution().maxSubarraySum(nums = [7, 1, 4, 5, 8, 2, 3, 6, 10, 11], k = 5) == 57

Answer: assert Solution().maxSubarraySum(nums = [1000000000, -1000000000, 1000000000, -1000000000, 1000000000, -1000000000], k = 3) == 1000000000

Answer: assert Solution().maxSubarraySum(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], k = 5) == 55

Answer: assert Solution().maxSubarraySum(nums = [1000000000, -1000000000, 2000000000, -2000000000, 3000000000, -3000000000], k = 2) == 2000000000

Answer: assert Solution().maxSubarraySum(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], k = 3) == 54

Answer: assert Solution().maxSubarraySum(nums = [5, 15, -10, 20, 30, -5, 10, 25, -20, 15], k = 3) == 80

Answer: assert Solution().maxSubarraySum(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], k = 25) == 25

Answer: assert Solution().maxSubarraySum(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], k = 5) == 75

Answer: assert Solution().maxSubarraySum(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150], k = 5) == 1200

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

Answer: assert Solution().maxSubarraySum(nums = [10, -5, 20, -15, 30, -25, 40, -35, 50, -45], k = 3) == 70

Answer: assert Solution().maxSubarraySum(nums = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5], k = 6) == 15

Answer: assert Solution().maxSubarraySum(nums = [-999999999, 999999999, -999999999, 999999999, -999999999, 999999999], k = 2) == 0

Answer: assert Solution().maxSubarraySum(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 7) == 490

Answer: assert Solution().maxSubarraySum(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], k = 10) == 465

Answer: assert Solution().maxSubarraySum(nums = [5, 2, -3, 1, 4, 8, -10, 100, -50, 20, 30, -20, 15, -15], k = 5) == 103

Answer: assert Solution().maxSubarraySum(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], k = 20) == 0

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

Answer: assert Solution().maxSubarraySum(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], k = 3) == 0

Answer: assert Solution().maxSubarraySum(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1], k = 6) == 0

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

Answer: assert Solution().maxSubarraySum(nums = [-50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140], k = 5) == 1050

Answer: assert Solution().maxSubarraySum(nums = [1000000000, -500000000, 250000000, -125000000, 62500000, -31250000, 15625000, -7812500, 3906250, -1953125], k = 5) == 687500000

Answer: assert Solution().maxSubarraySum(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], k = 7) == 14

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

Answer: assert Solution().maxSubarraySum(nums = [1000000000, -500000000, 1000000000, -500000000, 1000000000, -500000000, 1000000000, -500000000, 1000000000, -500000000], k = 2) == 2500000000

Answer: assert Solution().maxSubarraySum(nums = [5, -3, 1, 3, -2, 2, 4, -1, 5], k = 3) == 14

Answer: assert Solution().maxSubarraySum(nums = [5, 4, -1, 7, 8, -10, 100, -50, 20, -20, 30, -30], k = 6) == 108

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

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

Answer: assert Solution().maxSubarraySum(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], k = 13) == 247

Answer: assert Solution().maxSubarraySum(nums = [0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], k = 4) == 0

Answer: assert Solution().maxSubarraySum(nums = [5, -3, 8, -6, 2, 3, -1, 4, 7, -2, 10], k = 4) == 19

Answer: assert Solution().maxSubarraySum(nums = [-20, 15, -10, 25, -30, 35, -40, 45, -50, 55, -60, 65, -70, 75, -80, 85, -90, 95, -100, 105], k = 6) == 55

Answer: assert Solution().maxSubarraySum(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], k = 10) == 55

Answer: assert Solution().maxSubarraySum(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], k = 5) == 20

Answer: assert Solution().maxSubarraySum(nums = [-9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9], k = 5) == 45

Answer: assert Solution().maxSubarraySum(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500], k = 7) == 11900

Answer: assert Solution().maxSubarraySum(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], k = 5) == 0

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

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

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

Answer: assert Solution().maxSubarraySum(nums = [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], k = 5) == -5

Answer: assert Solution().maxSubarraySum(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200], k = 6) == 7800

Answer: assert Solution().maxSubarraySum(nums = [5, -3, 2, 1, 7, -4, 6, -2, 8, -5], k = 3) == 20

Answer: assert Solution().maxSubarraySum(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], k = 7) == 0

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

Answer: assert Solution().maxSubarraySum(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], k = 7) == 119

Answer: assert Solution().maxSubarraySum(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000], k = 8) == 20000

Answer: assert Solution().maxSubarraySum(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], k = 1) == 0

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

Answer: assert Solution().maxSubarraySum(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], k = 5) == 210

Answer: assert Solution().maxSubarraySum(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000], k = 5) == 5500

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

Answer: assert Solution().maxSubarraySum(nums = [-100, -200, -300, -400, -500, -600, -700, -800, -900, -1000], k = 5) == -1500

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

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

Answer: assert Solution().maxSubarraySum(nums = [3, 1, -4, 6, 2, -2, 5, -1, 4, -3, 7, 8], k = 3) == 26

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

Answer: assert Solution().maxSubarraySum(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1], k = 10) == 0

Answer: assert Solution().maxSubarraySum(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 5) == 550

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

Answer: assert Solution().maxSubarraySum(nums = [-1000000000, -2000000000, -3000000000, -4000000000, -5000000000], k = 2) == -3000000000

Answer: assert Solution().maxSubarraySum(nums = [5, -1, 5, -1, 5, -1, 5, -1], k = 3) == 12

Answer: assert Solution().maxSubarraySum(nums = [-1000000000, 1000000000, -1000000000, 1000000000, -1000000000, 1000000000], k = 6) == 0

Answer: assert Solution().maxSubarraySum(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], k = 4) == 210

Answer: assert Solution().maxSubarraySum(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000], k = 10) == 5500

Answer: assert Solution().maxSubarraySum(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], k = 20) == 0

Answer: assert Solution().maxSubarraySum(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], k = 7) == 189

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

Answer: assert Solution().maxSubarraySum(nums = [10, -10, 20, -20, 30, -30, 40, -40, 50, -50, 60, -60, 70, -70, 80, -80], k = 6) == 60

Answer: assert Solution().maxSubarraySum(nums = [3, 5, 7, 2, 8, 6, 4, 1, 9], k = 3) == 45

Answer: assert Solution().maxSubarraySum(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], k = 10) == 30

Answer: assert Solution().maxSubarraySum(nums = [10, -20, 30, -40, 50, -60, 70, -80, 90, -100, 110, -120], k = 6) == 30

Answer: assert Solution().maxSubarraySum(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], k = 5) == 55

Answer: assert Solution().maxSubarraySum(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000], k = 3) == 6000000000

Answer: assert Solution().maxSubarraySum(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1], k = 2) == 0

Answer: assert Solution().maxSubarraySum(nums = [1000000000, -999999999, 999999998, -999999997, 999999996, -999999995, 999999994, -999999993, 999999992, -999999991], k = 5) == 999999998

Answer: assert Solution().maxSubarraySum(nums = [10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100], k = 7) == 945

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

Answer: assert Solution().maxSubarraySum(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000], k = 5) == 10000000000

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

Answer: assert Solution().maxSubarraySum(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50], k = 6) == 225

Answer: assert Solution().maxSubarraySum(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], k = 5) == 0

Answer: assert Solution().maxSubarraySum(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], k = 3) == 465

Answer: assert Solution().maxSubarraySum(nums = [-5, -10, -15, -20, -25, -30, -35, -40, -45, -50], k = 5) == -75

Answer: assert Solution().maxSubarraySum(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1], k = 4) == 0

Answer: assert Solution().maxSubarraySum(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200], k = 10) == 2100

Answer: assert Solution().maxSubarraySum(nums = [10, -10, 20, -20, 30, -30, 40, -40, 50, -50], k = 5) == 50

Answer: assert Solution().maxSubarraySum(nums = [-100, 50, -30, 20, -10, 5, -3, 2, -1, 4, -6, 8, -10, 12, -14, 16, -18, 20, -22, 24], k = 5) == 43

Answer: assert Solution().maxSubarraySum(nums = [-1000000000, -1000000000, -1000000000, -1000000000, -1000000000], k = 1) == -1000000000

Answer: assert Solution().maxSubarraySum(nums = [-1, 3, -2, 5, 7, -8, 2, 4, -5, 6], k = 4) == 13

Answer: assert Solution().maxSubarraySum(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9], k = 4) == 44

Answer: assert Solution().maxSubarraySum(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], k = 4) == 8

Answer: assert Solution().maxSubarraySum(nums = [10, -10, 20, -20, 30, -30, 40, -40, 50, -50, 60, -60], k = 6) == 30

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 maxSubarraySum(self, nums: List[int], k: int) -> int:
        f = [inf] * k
        ans = -inf
        s = f[-1] = 0
        for i, x in enumerate(nums):
            s += x
            ans = max(ans, s - f[i % k])
            f[i % k] = min(f[i % k], s)
        return ans