You are given a garland consisting of $n$ lamps. States of the lamps are represented by the string $s$ of length $n$. The $i$-th character of the string $s_i$ equals '0' if the $i$-th lamp is turned off or '1' if the $i$-th lamp is turned on. You are also given a positive integer $k$.

In one move, you can choose one lamp and change its state (i.e. turn it on if it is turned off and vice versa).

The garland is called $k$-periodic if the distance between each pair of adjacent turned on lamps is exactly $k$. Consider the case $k=3$. Then garlands "00010010", "1001001", "00010" and "0" are good but garlands "00101001", "1000001" and "01001100" are not. Note that the garland is not cyclic, i.e. the first turned on lamp is not going after the last turned on lamp and vice versa.

Your task is to find the minimum number of moves you need to make to obtain $k$-periodic garland from the given one.

You have to answer $t$ independent test cases.


-----Input-----

The first line of the input contains one integer $t$ ($1 \le t \le 25~ 000$) — the number of test cases. Then $t$ test cases follow.

The first line of the test case contains two integers $n$ and $k$ ($1 \le n \le 10^6; 1 \le k \le n$) — the length of $s$ and the required period. The second line of the test case contains the string $s$ consisting of $n$ characters '0' and '1'.

It is guaranteed that the sum of $n$ over all test cases does not exceed $10^6$ ($\sum n \le 10^6$).


-----Output-----

For each test case, print the answer — the minimum number of moves you need to make to obtain $k$-periodic garland from the given one.


-----Example-----
Input
6
9 2
010001010
9 3
111100000
7 4
1111111
10 3
1001110101
1 1
1
1 1
0

Output
1
2
5
4
0
0

```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

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "from collections import defaultdict as dd\nfrom collections import deque\nimport bisect\nimport heapq\n\ndef ri():\n    return int(input())\n\ndef rl():\n    return list(map(int, input().split()))\n\n\ndef solve():\n    n, k = rl()\n    S = input()\n    zero_blocks = dd(int)\n    cost_all_zeros = 0\n    rem = 0\n    for i, c in enumerate(S):\n        if c == '1':\n            cost_all_zeros += 1\n            zero_blocks[rem] += 1\n        rem += 1\n        if rem == k:\n            rem = 0\n\n    global_best = n\n    for offset in range(k):\n        zero_others = cost_all_zeros - zero_blocks[offset]\n\n        pre, mid, post = 0, n, n\n        for i in range(offset, n, k):\n            if S[i] == '1':\n                new_pre = pre + 1\n                new_mid = min(mid, pre)\n                new_post = min(post + 1, mid + 1)\n            else:\n                new_pre = pre\n                new_mid = min(mid + 1, pre + 1)\n                new_post = min(post, mid)\n            pre, mid, post = new_pre, new_mid, new_post\n        best = min(pre, mid, post)\n\n        # print (offset, zero_others)\n        # print (pre, mid, post)\n        global_best = min(global_best, best + zero_others)\n\n\n    print (global_best)\n    # print ()\n\n\n\nmode = 'T'\n\nif mode == 'T':\n    t = ri()\n    for i in range(t):\n        solve()\nelse:\n    solve()\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14079