K-periodic Garland

题意翻译

给一个长度为 $n$ 的 01 字符串，要让这个字符串的每个 1 之间的距离恰好都为 $k$ ，请问至少要修改几个字符。

题目描述

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.

输入输出格式

输入格式

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 $ ).

输出格式

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.

输入输出样例

输入样例 #1

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

输出样例 #1

1
2
5
4
0
0