In an array A containing only 0s and 1s, a K-bit flip consists of choosing a (contiguous) subarray of length K and simultaneously changing every 0 in the subarray to 1, and every 1 in the subarray to 0.
Return the minimum number of K-bit flips required so that there is no 0 in the array.  If it is not possible, return -1.
 
Example 1:
Input: A = [0,1,0], K = 1
Output: 2
Explanation: Flip A[0], then flip A[2].


Example 2:
Input: A = [1,1,0], K = 2
Output: -1
Explanation: No matter how we flip subarrays of size 2, we can't make the array become [1,1,1].


Example 3:
Input: A = [0,0,0,1,0,1,1,0], K = 3
Output: 3
Explanation:
Flip A[0],A[1],A[2]: A becomes [1,1,1,1,0,1,1,0]
Flip A[4],A[5],A[6]: A becomes [1,1,1,1,1,0,0,0]
Flip A[5],A[6],A[7]: A becomes [1,1,1,1,1,1,1,1]

 


Note:

1 <= A.length <= 30000
1 <= K <= A.length

```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 = 'class Solution:\n    def minKBitFlips(self, A: List[int], K: int) -> int:\n        l = len(A)\n        rem = l % K\n        # find indexes where the number changes\n        # add to change_list based on remainder class mod K\n        prev = 1\n        change_list = [[] for i in range(K)]\n        for ind, num in enumerate(A):\n            if prev != num:\n                prev = num\n                change_list[ind % K].append(ind)\n        if num == 0:\n            change_list[rem].append(l)\n    \n        num_flips = 0\n        \n        for r, mini_list in enumerate(change_list):\n            mini_list_len = len(mini_list)\n            if mini_list_len % 2 == 1:\n                return -1\n            for i in range(mini_list_len // 2):\n                first = mini_list.pop(0)\n                second = mini_list.pop(0)\n                num_flips += (second - first) // K\n        \n        return num_flips\n        \n        \n        \n        \n    \n    \n    def oldMinKBitFlips(self, A: List[int], K: int) -> int:\n        l = len(A)\n        \n        # find indexes where the number changes\n        prev = 1\n        change_list = []\n        for ind, num in enumerate(A):\n            if prev != num:\n                prev = num\n                change_list.append(ind)\n        \n        if len(change_list) == 0:\n            return 0\n        \n        num_flips = 0\n\n        while len(change_list) > 1:\n            first = change_list[0]\n            # if first + K > l, we are doomed\n            if first + K >= l:\n                return -1\n            # remove first, and either\n                # 1) remove first + K if it exists, or\n                # 2) add first + K if it does not exist\n            change_list = change_list[1:]\n            left_insertion_pt = bisect.bisect_left(change_list, first + K)\n            if left_insertion_pt >= len(change_list):\n                change_list.append(first + K)\n            elif change_list[left_insertion_pt] == first + K:\n                del change_list[left_insertion_pt]\n            else:\n                change_list.insert(left_insertion_pt, first+K)\n            num_flips += 1\n            \n            \n        if len(change_list) > 0:\n            # in this section, len(change_list) == 1\n            first = change_list[0]\n            q, r = divmod(l - first, K)\n            if r == 0:\n                return num_flips + q\n            else:\n                return -1\n            \n        return num_flips'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'minKBitFlips'
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: 5922