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.math.BigInteger; 
import java.util.*;
import java.math.*; 

//Mann Shah [ DAIICT ].
//fast io

public class Main {
	static long mod = (long) (1e9+7);
	static long mm = (long)(1e9+6);
	static long N = (long)(2*1e5);
	static InputReader in;
    static PrintWriter out;
    static Debugger deb;
    
    
    public static int lower_bound(long[] a,int k) { // no. of elements less than k in array.
    		int first = 0,last = a.length,mid;
        while (first < last) {
            mid = first + ((last - first) >> 1); 
            if (a[mid] < k)  //lower bound. for upper use <= ( n - first)
                first = mid + 1; 
            else 
                last = mid;
        }
    		return first;
    }
    
    public static long gcd(long a, long b){ 
	    if (a == 0) 
	        return b;  
	    return gcd(b % a, a);  
    } 
    
    public static long power(long x, long y, long p) 
    { 
        long res = 1;      
        x = x % p;  
       if (x == 0) return 0; 
        while (y > 0) { 
            if((y & 1)==1) 
                res = (res * x) % p;
            y = y >> 1;  
            x = (x * x) % p;  
        } 
        return res; 
    }     
    
    	public static void main(String args[] ) throws NumberFormatException, IOException  {
			
		in = new InputReader(System.in);
	    out = new PrintWriter(System.out);
	    deb = new Debugger();
	    
	    int T = in.nextInt();
	    while(T-->0) {
	    		int n = in.nextInt();
		    int k = in.nextInt();
		    
		    char[] s = in.readString().toCharArray();
		    
		    int[] pre = new int[n];
		    pre[0] = s[0]-'0';
		    for(int i=1;i<n;i++) {
		    		pre[i] = pre[i-1]+(s[i]-'0');
		    }
	
		    int[] dp = new int[n];
		    for(int i=n-1;i>=0;i--) {
		    		int c =0;
		    		if(s[i]=='0') {
		    			c+=1;
		    		}
		    		c+=pre[i+k-1<n ? i+k-1 : n-1]-pre[i]; //taking prev 1 to 0 
		    		if(i+k<n) {
		    			c+=dp[i+k];
		    		}
		    		
		    		//making all 0
		    		int cv = pre[n-1]-pre[i]+s[i]-'0';
		    		dp[i] = Math.min(cv, c);
		    }
		    
		    int min = dp[0];
		    for(int i=1;i<n;i++) {
		    		min = Math.min(min, dp[i]+pre[i-1]);
		    }
		    out.println(min);
	    }
	    
	    
	    
	    out.close();
	}
		
/* TC space



 */	
		static class InputReader
	    {
	        private final InputStream stream;
	        private final byte[] buf = new byte[8192];
	        private int curChar, snumChars;
	        private SpaceCharFilter filter;

	        public InputReader(InputStream stream)
	        {
	                this.stream = stream;
	        }

	        public int snext()
	        {
	                if (snumChars == -1)
	                        throw new InputMismatchException();
	                if (curChar >= snumChars)
	                {
	                        curChar = 0;
	                        try
	                        {
	                                snumChars = stream.read(buf);
	                        } catch (IOException e)
	                        {
	                                throw new InputMismatchException();
	                        }
	                        if (snumChars <= 0)
	                                return -1;
	                }
	                return buf[curChar++];
	        }

	        public int nextInt()
	        {
	                int c = snext();
	                while (isSpaceChar(c))
	                {
	                        c = snext();
	                }
	                int sgn = 1;
	                if (c == '-')
	                {
	                        sgn = -1;
	                        c = snext();
	                }
	                int res = 0;
	                do
	                {
	                        if (c < '0' || c > '9')
	                                throw new InputMismatchException();
	                        res *= 10;
	                        res += c - '0';
	                        c = snext();
	                } while (!isSpaceChar(c));
	                return res * sgn;
	        }

	        public long nextLong()
	        {
	                int c = snext();
	                while (isSpaceChar(c))
	                {
	                        c = snext();
	                }
	                int sgn = 1;
	                if (c == '-')
	                {
	                        sgn = -1;
	                        c = snext();
	                }
	                long res = 0;
	                do
	                {
	                        if (c < '0' || c > '9')
	                                throw new InputMismatchException();
	                        res *= 10;
	                        res += c - '0';
	                        c = snext();
	                } while (!isSpaceChar(c));
	                return res * sgn;
	        }

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

	        public long[] nextLongArray(int n)
	        {
	                long a[] = new long[n];
	                for (int i = 0; i < n; i++)
	                {
	                        a[i] = nextLong();
	                }
	                return a;
	        }
	        
	        public ArrayList<Integer> nextArrayList(int n){
	        			ArrayList<Integer> x = new ArrayList<Integer>();
	        			for(int i=0;i<n;i++) {
	        				int v = in.nextInt();
	        				x.add(v);
	        			}
	        			return x;
	        }

	        public String readString()
	        {
	                int c = snext();
	                while (isSpaceChar(c))
	                {
	                        c = snext();
	                }
	                StringBuilder res = new StringBuilder();
	                do
	                {
	                        res.appendCodePoint(c);
	                        c = snext();
	                } while (!isSpaceChar(c));
	                return res.toString();
	        }

	        public String nextLine()
	        {
	                int c = snext();
	                while (isSpaceChar(c))
	                        c = snext();
	                StringBuilder res = new StringBuilder();
	                do
	                {
	                        res.appendCodePoint(c);
	                        c = snext();
	                } while (!isEndOfLine(c));
	                return res.toString();
	        }

	        public boolean isSpaceChar(int c)
	        {
	                if (filter != null)
	                        return filter.isSpaceChar(c);
	                return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	        }

	        private boolean isEndOfLine(int c)
	        {
	                return c == '\n' || c == '\r' || c == -1;
	        }

	        public interface SpaceCharFilter
	        {
	                public boolean isSpaceChar(int ch);
	        }

	    }
		
		static class Debugger{
			public void n(int x) {
				out.println(x);
			}
			
			public void a(int[] a) {
		        StringBuilder sb = new StringBuilder();
		        for(int i=0;i<a.length;i++) {
		        		sb.append(a[i]+" ");
		        }
		        out.println(sb.toString());
			}
		}
		
}


 class Pair { 
    int x; 
    int y; 
    // Constructor 
    public Pair(int x, int y) 
    { 
        this.x = x; 
        this.y = y; 
    } 
	@Override
	public boolean equals(Object o) {
	    if (this == o) return true;
	    if (!(o instanceof Pair)) return false;
	    Pair p = (Pair) o;
	    return x == p.x && y == p.y;
	}	
	@Override
	public int hashCode() {
		return (""+x+"-"+y).hashCode();
	}
	
} 