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.lang.reflect.Array;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.text.DecimalFormat;
import java.util.*;
import java.util.regex.Matcher;
import java.util.regex.Pattern;

public class Main
{	
   //static long mod=(long)(1e+9 + 7);
   static long mod=(long)998244353;
   
   static int[] sieve;
   static ArrayList<Integer> primes;
   static PrintWriter out;
   static fast s;
   static StringBuilder fans;
   
   static int x_dir[];
   static int y_dir[];

   public static void solve()
   {
   	int n=s.nextInt();
   	int k=s.nextInt();
   	
   	int a[]=new int[n];
   	String str=s.nextLine();
   	for(int i=0;i<str.length();i++) a[i]=str.charAt(i)-'0';
   	
   	int ones[]=new int[n];
   	if(a[0]==1) ones[0]=1;
   	
   	for(int i=1;i<n;i++) 
   		if(a[i]==1) ones[i]=1+ones[i-1];
   	   else ones[i]=ones[i-1];
   	
   	long dp[][]=new long[n][2];
   	long ans=0;
   	
   	if(a[0]==0) dp[0][1]=1;
   	else dp[0][0]=1;
   	
   	for(int i=1;i<n;i++)
   		{
   			if(a[i]==0)
   				{
   					dp[i][0]=Math.min(dp[i-1][0], dp[i-1][1]);
   					
   					long prev_dp=((i-k)>=0)?dp[i-k][1]:0;
   					long prev_ones=((i-k)>=0)?ones[i-k]:0;
   					dp[i][1]=1+Math.min(prev_dp+(ones[i-1]-prev_ones),ones[i-1]);
   				}
   			else
   				{
   					long prev_dp=((i-k)>=0)?dp[i-k][1]:0;
   					long prev_ones=((i-k)>=0)?ones[i-k]:0;
   					dp[i][1]=Math.min(prev_dp+(ones[i-1]-prev_ones),ones[i-1]);
   					dp[i][0]=1+Math.min(dp[i-1][0], dp[i-1][1]);
   				}
   		}
   	
   	ans=Math.min(dp[n-1][0], dp[n-1][1]);
   	fans.append(ans+"\n");
   }
   
   public static void main(String[] args) throws java.lang.Exception
   {	  	
	     s = new fast();
	     
	     out=new PrintWriter(System.out);
	     fans=new StringBuilder("");
		  
	     int t=s.nextInt();
	     
	     while(t>0)
	    	 {
	    		 solve();
	    		 t--;
	    	 }
	    
	    out.println(fans);
	    out.close();
   }
  
 
 
static class fast {   
	
	   private InputStream i;
		private byte[]  buf = new byte[1024];
		private int curChar;
		
		private int numChars;
		
		//Return floor log2n
		public static long log2(long bits) // returns 0 for bits=0
			{
			    int log = 0;
			    if( ( bits & 0xffff0000 ) != 0 ) { bits >>>= 16; log = 16; }
			    if( bits >= 256 ) { bits >>>= 8; log += 8; }
			    if( bits >= 16  ) { bits >>>= 4; log += 4; }
			    if( bits >= 4   ) { bits >>>= 2; log += 2; }
			    return log + ( bits >>> 1 );
			}
		
		public static boolean next_permutation(int a[])
		   {
			   int i=0,j=0;int index=-1;	   
			   int n=a.length;
			   
			   for(i=0;i<n-1;i++)
				   if(a[i]<a[i+1]) index=i;
			   
			   if(index==-1) return false;
			   i=index;
 
			  
			   for(j=i+1;j<n && a[i]<a[j];j++);
 
			   int temp=a[i];
			   a[i]=a[j-1];
			   a[j-1]=temp;
			   	   
			   for(int p=i+1,q=n-1;p<q;p++,q--)
			   {
				   temp=a[p];
				   a[p]=a[q];
				   a[q]=temp;
			   }
			   
			   return true;
		   }
		   
		public static void sieve(int size)
		{
			sieve=new int[size+1];
			
			primes=new ArrayList<Integer>();
			
			sieve[1]=1;
			
			for(int i=2;i*i<=size;i++)
			{
				if(sieve[i]==0)
				 {
					for(int j=i*i;j<size;j+=i) {sieve[j]=1;}
				 }
			}
			
			for(int i=2;i<=size;i++)
			{
				if(sieve[i]==0) primes.add(i);
			}
		}
		
		public static long pow(long a, long p){
		    long o = 1;
		    for(; p>0; p>>=1){
		        if((p&1)==1)o = mul(o, a);
		        a = mul(a, a);
		    }
		    return o;
		}
		
		public static long add(long... a){
		    long o = 0;
		    for(long x:a)o = (o+mod+x)%mod;
		    return o;
		}
		
		public static long mul(long... a){
		    long p = 1;
		    for(long x:a)p = (mod+(p*x)%mod)%mod;
		    return p;
		}
		
		public static long mod_inv(long n)
		{
			return pow(n,mod-2);
		}
		   
		public long gcd(long r,long ans)
		{
			if(r==0) return ans;
			return gcd(ans%r,r);
		}
		
		public fast() {
			this(System.in);
		}
		public fast(InputStream is) {
			i = is;
		}
		public int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = i.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
		public String nextLine() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}
		public String nextString() {
     		int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}
		public long nextLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
		public int nextInt() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
		public boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
		public boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}
 
	}	
}