You are given a string s containing lowercase letters and an integer k. You need to :

First, change some characters of s to other lowercase English letters.
Then divide s into k non-empty disjoint substrings such that each substring is palindrome.

Return the minimal number of characters that you need to change to divide the string.
 
Example 1:
Input: s = "abc", k = 2
Output: 1
Explanation: You can split the string into "ab" and "c", and change 1 character in "ab" to make it palindrome.

Example 2:
Input: s = "aabbc", k = 3
Output: 0
Explanation: You can split the string into "aa", "bb" and "c", all of them are palindrome.
Example 3:
Input: s = "leetcode", k = 8
Output: 0

 
Constraints:

1 <= k <= s.length <= 100.
s only contains lowercase English letters.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "'''\nDfs: either create new palindrome or expand\n\nIf expanding recurse down (num swaps and divides):\n- With a swap you add 1\n- Without, you don't add \n\nEdge of the pal has to be the next value\n\nj-i = 0\nj-i = 1\nj-i = 2\n\nCaching mechanism\n'''\nclass Solution:\n    def palindromePartition(self, s: str, k: int) -> int:\n        n = len(s)\n        memo = {}\n        \n        def cost(s,i,j): #calculate the cost of transferring one substring into palindrome string\n            r = 0\n            while i < j:\n                if s[i] != s[j]:\n                    r += 1\n                i += 1\n                j -= 1\n            return r\n        \n        def dfs(i, k):\n            if (i, k) in memo: return memo[(i, k)] #case already in memo\n            if n - i == k: #base case that each substring just have one character\n                return 0\n            if k == 1:    #base case that need to transfer whole substring into palidrome\n                return cost(s, i, n - 1)\n            res = float('inf')\n            for j in range(i + 1, n - k + 2): # keep making next part of substring into palidrome\n                res = min(res, dfs(j, k - 1) + cost(s,i, j - 1)) #compare different divisions to get the minimum cost\n            memo[(i, k)] = res\n            return res\n        return dfs(0 , k)\n            \n            \n#             for j in range(i, self.length):\n#                 t = self.dp.get((i,j+1))\n#                 if not t:\n#                     count = cost(i,j)\n#                 else:\n#                     count = t\n                \n\n#                 dfs(j+1,ch+count,nk-1) #  case where you split\n             \n#         dfs(0,0,k)\n\n#         return self.r\n                \n            \n            \n            \n            \n            \n# #         n = len(s)\n# #         memo = {}\n        \n# #         def cost(s,i,j): #calculate the cost of transferring one substring into palindrome string\n# #             r = 0\n# #             while i < j:\n# #                 if s[i] != s[j]:\n# #                     r += 1\n# #                 i += 1\n# #                 j -= 1\n# #             return r\n        \n# #         def dfs(i, k):\n# #             if (i, k) in memo: return memo[(i, k)] #case already in memo\n# #             if n - i == k: #base case that each substring just have one character\n# #                 return 0\n# #             if k == 1:    #base case that need to transfer whole substring into palidrome\n# #                 return cost(s, i, n - 1)\n# #             res = float('inf')\n# #             for j in range(i + 1, n - k + 2): # keep making next part of substring into palidrome\n# #                 res = min(res, dfs(j, k - 1) + cost(s,i, j - 1)) #compare different divisions to get the minimum cost\n# #             memo[(i, k)] = res\n# #             return res\n# #         return dfs(0 , k)\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'palindromePartition'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 6712