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 ≤ t ≤ 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 ≤ n ≤ 10^6; 1 ≤ k ≤ 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 (∑ n ≤ 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
import java.io.*;
import java.util.*;

import static java.lang.Math.*;

public class Main {

    static void run() throws IOException {
        file("", "");

        int t = nextInt();
        while (t-- > 0)
            solution();
        end();
    }


    static void solution() throws IOException {
        int n = nextInt();
        int k = nextInt();
        int all_ones = 0;
        int[] arr = new int[n];
        char[] h = nextToken().toCharArray();
        for (int i = 0; i < n; i++) {
            arr[i] = h[i] - 48;
            if (arr[i] == 1)
                all_ones++;
        }
        if (all_ones <= 1) {
            out.println(0);
            return;
        }
        int[] one = new int[n];
        int[] zero = new int[n];
        int ans = Integer.MAX_VALUE;
        for (int i = 0; i < n; i++) {
            if (i - k < 0) {
                if (arr[i] == 0)
                    zero[i]++;
                else
                    one[i]++;
            } else {
                if (arr[i] == 0) {
                    if (one[i - k] > zero[i - k]) {
                        one[i] = one[i - k];
                        zero[i] = zero[i - k]+1;
                    } else {
                        zero[i]++;
                    }
                } else {
                    if (one[i - k] > zero[i - k]) {
                        one[i] = one[i - k] + 1;
                        zero[i] = zero[i - k];
                    } else {
                        one[i]++;
                    }
                }
            }
            ans = min(ans, all_ones - one[i] + zero[i]);
        }

        out.println(ans);
    }

    static mem create_mem(int l, int r) {
        mem y = new mem();
        y.l = l;
        y.r = r;

        return y;
    }

    static class mem {
        int l, r;

    }


    static void Z_function() throws IOException {
        char[] s = nextToken().toCharArray();
        int[] z = new int[s.length];
        for (int i = 1, l = 0, r = 0; i < s.length; i++) {
            if (i <= r)
                z[i] = min(r - i + 1, z[i - l]);
            while (z[i] + i < s.length && s[z[i] + i] == s[z[i]])
                ++z[i];
            if (i + z[i] - 1 > r) {
                l = i;
                r = i + z[i] - 1;
            }
        }
        for (int i = 0; i < z.length; i++) {
            out.print(z[i] + " ");
        }
    }

    static long Pow(long a, long b) {
        long h = 1;
        while (b > 0) {
            if (b % 2 != 0) {
                h *= a;
                b--;
            }
            b /= 2;
            a *= a;
        }
        return h;
    }

    static long lcm(long a, long b) {
        return a * b / gcd(a, b);
    }

    static long gcd(long a, long b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    static void end() {
        out.flush();
        out.close();
    }

    static BufferedReader br;
    static PrintWriter out;

    static void file(String input, String output) {
        if (input.equals("")) {
            br = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            try {
                br = new BufferedReader(new FileReader(input));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
            try {
                out = new PrintWriter(output);
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }
    }

    static StringTokenizer in = new StringTokenizer("");

    public static String nextToken() throws IOException {
        while (in == null || !in.hasMoreTokens()) {
            String s = br.readLine();
            if (s == null) return null;
            in = new StringTokenizer(s);
        }
        return in.nextToken();
    }


    public static int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    public static double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    public static long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }


    public static void main(String[] args) throws IOException {
        run();
    }
}