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.util.*;
import java.io.*;

public class tr0 {
	static PrintWriter out;
	static StringBuilder sb;
	static int mod = (int) 1e9 + 7;
	static long inf = (long) 1e16;
	static int[] col;
	static int n, k, pre[];
	static ArrayList<Integer>[] ad;
	static int[][] memo;
	static ArrayList<Integer> h;
	static int[] perm;
	static char[] a;
	static boolean[] tak;
	static boolean f;

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		out = new PrintWriter(System.out);
		int t = sc.nextInt();
		while (t-- > 0) {
			n = sc.nextInt();
			k = sc.nextInt();
			a = sc.nextLine().toCharArray();
			memo = new int[n+k+1][2];
			pre = new int[n];
			int one = 0;
			for (int i = 0; i < n; i++) {
				if (a[i] == '1')
					one++;
				pre[i] = one;
			}
			for (int i = n - 1; i >= 0; i--) {
				for (int on = 0; on < 2; on++) {
					if (on == 0) {
						int v = 0;
						int o = 0;
						if (a[i] == '1')
							v++;
						else
							o++;
						int kv = 0;
						if (i + k < n)
							kv = pre[i + k - 1] - pre[i];
						else {
							kv = pre[n - 1] - pre[i];
						}

						memo[i][on] = Math.min(memo[i + 1][0] + v, memo[i + k][1] + kv + o);
					} else {
						int v = 0;
						int o = 0;
						if (a[i] == '1')
							v++;
						else
							o++;
						int kv = 0;
						if (i + k < n)
							kv = pre[i + k - 1] - pre[i];
						else {
							kv = pre[n - 1] - pre[i];
						}
						int kl = pre[n - 1] - pre[i];
						memo[i][on] = Math.min(kl + v, memo[i + k][1] + kv + o);
					}
				}
			}
			out.println(memo[0][0]);
		}
		out.flush();
	}

	static int dp(int i, int on) {
//		System.out.println(i+" "+on);
		if (i >= n)
			return 0;
		if (memo[i][on] != -1)
			return memo[i][on];
		int ans = Integer.MAX_VALUE;
		if (on == 0) {
			int v = 0;
			int o = 0;
			if (a[i] == '1')
				v++;
			else
				o++;
			int kv = 0;
			if (i + k < n)
				kv = pre[i + k - 1] - pre[i];
			else {
				kv = pre[n - 1] - pre[i];
			}

			ans = Math.min(dp(i + 1, 0) + v, dp(i + k, 1) + kv + o);
		} else {
			int v = 0;
			int o = 0;
			if (a[i] == '1')
				v++;
			else
				o++;
			int kv = 0;
			if (i + k < n)
				kv = pre[i + k - 1] - pre[i];
			else {
				kv = pre[n - 1] - pre[i];
			}
			int kl = pre[n - 1] - pre[i];
			ans = Math.min(kl + v, dp(i + k, 1) + kv + o);
		}
		return memo[i][on] = ans;
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

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

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

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

		public Long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public int[] nextArrInt(int n) throws IOException {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		public long[] nextArrLong(int n) throws IOException {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}