Polycarp and his friends want to visit a new restaurant. The restaurant has n tables arranged along a straight line. People are already sitting at some tables. The tables are numbered from 1 to n in the order from left to right. The state of the restaurant is described by a string of length n which contains characters "1" (the table is occupied) and "0" (the table is empty).

Restaurant rules prohibit people to sit at a distance of k or less from each other. That is, if a person sits at the table number i, then all tables with numbers from i-k to i+k (except for the i-th) should be free. In other words, the absolute difference of the numbers of any two occupied tables must be strictly greater than k.

For example, if n=8 and k=2, then:

  * strings "10010001", "10000010", "00000000", "00100000" satisfy the rules of the restaurant; 
  * strings "10100100", "10011001", "11111111" do not satisfy to the rules of the restaurant, since each of them has a pair of "1" with a distance less than or equal to k=2. 



In particular, if the state of the restaurant is described by a string without "1" or a string with one "1", then the requirement of the restaurant is satisfied.

You are given a binary string s that describes the current state of the restaurant. It is guaranteed that the rules of the restaurant are satisfied for the string s.

Find the maximum number of free tables that you can occupy so as not to violate the rules of the restaurant. Formally, what is the maximum number of "0" that can be replaced by "1" such that the requirement will still be satisfied?

For example, if n=6, k=1, s= "100010", then the answer to the problem will be 1, since only the table at position 3 can be occupied such that the rules are still satisfied.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases in the test. Then t test cases follow.

Each test case starts with a line containing two integers n and k (1 ≤ k ≤ n ≤ 2⋅ 10^5) — the number of tables in the restaurant and the minimum allowed distance between two people.

The second line of each test case contains a binary string s of length n consisting of "0" and "1" — a description of the free and occupied tables in the restaurant. The given string satisfy to the rules of the restaurant — the difference between indices of any two "1" is more than k.

The sum of n for all test cases in one test does not exceed 2⋅ 10^5.

Output

For each test case output one integer — the number of tables that you can occupy so as not to violate the rules of the restaurant. If additional tables cannot be taken, then, obviously, you need to output 0.

Example

Input


6
6 1
100010
6 2
000000
5 1
10101
3 1
001
2 2
00
1 1
0


Output


1
2
0
1
1
1

Note

The first test case is explained in the statement.

In the second test case, the answer is 2, since you can choose the first and the sixth table.

In the third test case, you cannot take any free table without violating the rules of the restaurant.
//package cp;
import java.util.*;


import static java.lang.Math.min;
import static java.lang.Math.abs;
import static java.lang.Math.max;
import java.io.*;
 
public class Codechef {
	static long[] mods = {1000000007, 998244353, 1000000009};
	static long mod = mods[0];
	public static MyScanner in;
    public static PrintWriter out;
    static int[][] dp;
    
    
	public static void main( String[] args ) throws IOException{
		
 		in = new MyScanner();
 		out = new PrintWriter(System.out);
 		StringBuilder ans1=new StringBuilder();
		int test=in.nextInt();
		while(test-->0) {
			//StringBuilder ans=new StringBuilder();
			int n=in.nextInt();
			int k=in.nextInt();
			char ch[]=in.next().toCharArray();
			long ans=0;
			
			int i=0;
               while(i<n){
                    int pos=i;
                    if(ch[i]=='0'){
                         for(int j=i;j<n && j<=i+k;j++)
                              if(ch[j]=='1')  pos=j;
                          
                         if(pos==i)  ans++;
                         }
                    i=pos+k+1;
               }
			
			ans1.append(ans).append(System.getProperty("line.separator"));
		}
		
		out.println(ans1);
 		out.close();
 		
 	}
	
	public static boolean check(char[] ch, int i, int k) {
		if(i>=k) {
			for(int j=i-1;j>=i-k;j--) {
				if(ch[j]=='1')	return false;
			}
		}else {
			for(int j=i-1;j>=0;j--) {
				if(ch[j]=='1')	return false;
			}
		}
		if(ch.length-1-i>=k) {
			for(int j=i+1;j<i+k;j++) {
				if(ch[j]=='1')	return false;
			}
		}else {
			for(int j=i+1;j<ch.length;j++) {
				if(ch[j]=='1')	return false;
			}
		}
		return true;
	}
	
	//sorted check in non decreasing order
	static boolean isSorted(long arr[], int n){
       if (n == 0 || n == 1)      return true;
       for (int i = 1; i < n; i++)
           if (arr[i - 1] > arr[i])    return false;
       return true;
    }
	
	
	static long lcm_comp(long a, long b) {	return (a / gcd_comp(a, b)) * b;	}
 
	static long gcd_comp(long a, long b){
        if (a == 0)		return b;
        if (b == 0)		return a;
        long k;
        for (k = 0; ((a | b) & 1) == 0; ++k){
            a >>= 1;
            b >>= 1;
        }
        while ((a & 1) == 0)	a >>= 1;  
        do{
            while ((b & 1) == 0)	 b >>= 1;
            if (a > b){    
                long temp = a;
                a = b;
                b = temp;
            }
            b = (b - a);
        } while (b != 0);
        return a << k;
    }

	
	//comparator to solve according to b in descending order
	static class Pair implements Comparable<Pair>{
		private long a;
		private long b;
		public Pair(long a, long b) {
			this.a = a;
			this.b = b;
		}
		public int compareTo(Pair other) {
			return Long.compare(this.b, other.b );		//to sort in ascending order swap the arguments in Long.compare
			//return Long.compare(other.b ,this.b); 	//to sort in descending order swap the arguments in Long.compare
		}
	}
	
	static void printArray(long[] a) {
		StringBuilder stringBuilder=new StringBuilder();
		for(long i: a)	stringBuilder.append(i).append(" ");
		out.println(stringBuilder);
	}
	
	public static void sort(long[] array){
		ArrayList<Long> copy = new ArrayList<>();
		for (long i : array)
			copy.add(i);
		Collections.sort(copy);
		for(int i = 0;i<array.length;i++)
			array[i] = copy.get(i);
	}
	
	public static void sortDes(long[] array){
		ArrayList<Long> copy = new ArrayList<>();
		for (long i : array)
			copy.add(i);
		Collections.sort(copy);
		int j=array.length-1;
		for(int i = 0;i<array.length;i++)
			array[j--] = copy.get(i);
	}
	
	
	static String[] readArrayString(int n){
		String[] array = new String[n];
		for(int j =0 ;j<n;j++)
			array[j] = in.next();
		return array;
	}
	
	
	static int[] readArrayInt(int n){
    	int[] array = new int[n];
    	for(int j = 0;j<n;j++)
    		array[j] = in.nextInt();
    	return array;
    }
	
	static int[] readArrayInt1(int n){
		int[] array = new int[n+1];
		for(int j = 1;j<=n;j++){
			array[j] = in.nextInt();
		}
		return array;
	}
	
	static long[] readArrayLong(int n){
		long[] array = new long[n];
		for(int j =0 ;j<n;j++)
			array[j] = in.nextLong();
		return array;
	}
	
	static double[] readArrayDouble(int n){
		double[] array = new double[n];
		for(int j =0 ;j<n;j++)
			array[j] = in.nextDouble();
		return array;
	}
	
	static int minIndex(int[] array){
		int minValue = Integer.MAX_VALUE;
		int minIndex = -1;
		for(int j = 0;j<array.length;j++){
			if (array[j] < minValue){
				minValue = array[j];
				minIndex = j;
			}
		}
		return minIndex;
	}
	
	static int minIndex(long[] array){
		long minValue = Long.MAX_VALUE;
		int minIndex = -1;
		for(int j = 0;j<array.length;j++){
			if (array[j] < minValue){
				minValue = array[j];
				minIndex = j;
			}
		}
		return minIndex;
	}
	
	static int minIndex(double[] array){
		double minValue = Double.MAX_VALUE;
		int minIndex = -1;
		for(int j = 0;j<array.length;j++){
			if (array[j] < minValue){
				minValue = array[j];
				minIndex = j;
			}
		}
		return minIndex;
	}
	
	
	static int maxIndex(int[] array){
		int maxValue = Integer.MIN_VALUE;
		int maxIndex = -1;
		for(int j = 0;j<array.length;j++){
			if (array[j] > maxValue){
				maxValue = array[j];
				maxIndex = j;
			}
		}
		return maxIndex;
	}
	
	static int maxIndex(long[] array){
		long maxValue = Long.MIN_VALUE;
		int maxIndex = -1;
		for(int j = 0;j<array.length;j++){
			if (array[j] > maxValue){
				maxValue = array[j];
				maxIndex = j;
			}
		}
		return maxIndex;
	}
	
	
	static long power(long x, long y){
		if (y == 0)
			return 1;
		if (y%2 == 1)
			return (x*power(x, y-1))%mod;
		return power((x*x)%mod, y/2)%mod;
	}
	static void verdict(boolean a){
        out.println(a ? "YES" : "NO");
    }
	
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;
        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } 
                catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        int nextInt() {
            return Integer.parseInt(next());
        }
        long nextLong() {
            return Long.parseLong(next());
        }
        double nextDouble() {
            return Double.parseDouble(next());
        }
        String nextLine() {
            String str = "";
            try{
                str = br.readLine();
            } 
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        
    }	
}