You are given a binary string of length n (i. e. a string consisting of n characters '0' and '1').

In one move you can swap two adjacent characters of the string. What is the lexicographically minimum possible string you can obtain from the given one if you can perform no more than k moves? It is possible that you do not perform any moves at all.

Note that you can swap the same pair of adjacent characters with indices i and i+1 arbitrary (possibly, zero) number of times. Each such swap is considered a separate move.

You have to answer q independent test cases.

Input

The first line of the input contains one integer q (1 ≤ q ≤ 10^4) — the number of test cases.

The first line of the test case contains two integers n and k (1 ≤ n ≤ 10^6, 1 ≤ k ≤ n^2) — the length of the string and the number of moves you can perform.

The second line of the test case contains one string 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 on it: the lexicographically minimum possible string of length n you can obtain from the given one if you can perform no more than k moves.

Example

Input


3
8 5
11011010
7 9
1111100
7 11
1111100


Output


01011110
0101111
0011111

Note

In the first example, you can change the string as follows: 1\underline{10}11010 → \underline{10}111010 → 0111\underline{10}10 → 011\underline{10}110 → 01\underline{10}1110 → 01011110. 

In the third example, there are enough operations to make the string sorted.
//  package Jobeel;
import java.util.*;
import java.io.*;
import java.lang.*;
import java.math.*;
import java.util.Map.*;

public class codeforces {
	static int [] size,arr;
	static int inv;
   
	public static int find(int i) {
		if(arr[i]==i) return i;
		else {
			int result=find(arr[i]);
			arr[i]=result;
			return result;
		}
	}
public static void union(int u,int v) {
		int root_u=find(u);
		int root_v=find(v);
		if (root_u==root_v) return;
		else if(size[root_u]>size[root_v]) {
			size[root_u]+=size[root_v];
			arr[root_v]=root_u;
		}else  {
			size[root_v]+=size[root_u];
			arr[root_u]=root_v;
		}
	}
    static int search(int x,pair [] arr) {
    	int low=0,high=arr.length-1,ans=-1;
    	while(low<=high) {
    		int mid=(low+high)>>1;
    	    if(arr[mid].x>=x) {ans=mid; high=mid-1;}
    	    else low=mid+1;
    	}
    	return ans;
    }
   static  long gcd(long a, long b) 
    { 
        if (b == 0) 
            return a; 
        return gcd(b, a % b);  
          
    } 
   
       public static void main(String [] args) throws IOException, InterruptedException {
	     InputReader sc=new InputReader(System.in);
	     
	     int t=sc.nextInt(); 
	     while(t-->0) {
	    	 int x=sc.nextInt(); long k=sc.nextLong();
	    	 char [] ch=sc.next().toCharArray();
	    	int b=0;
	    	for(int i=0;i<x;i++){
	    		if(ch[i]=='0' && k>0){
	    			long min=Math.min(k,(long)i-b);
	    			char temp=ch[(int)(i-min)];
	    			ch[(int)(i-min)]=ch[i];
	    			ch[i]=temp;
	    			k-=min;
	    			b++;
	    		}
	    	}
	    	 
	    	 
	    	 pw.println(toString(ch, 0, x-1));
	     }
	     pw.flush();
		pw.close();
	}
	static class pair implements Comparable<pair>{
		String  name; int x,y ;
		
		
		public pair (int x,int y) {
			this.x=x; this.y=y;
		}
		public int compareTo(pair o) {
			return o.x-x;
		}
		public String toString() {
			return x+" "+y;
		}
	}

	static 	PrintWriter pw=new PrintWriter(System.out);
	public static StringBuilder toString(int [] arr,int l,int r) {
		StringBuilder sb=new StringBuilder();
		for(int i=l;i<=r;i++) sb.append(arr[i]+" ");
		return sb;
	}
	public static StringBuilder toString(long [] arr,int l,int r) {
		StringBuilder sb=new StringBuilder();
		for(int i=l;i<=r;i++) sb.append(arr[i]+" ");
		return sb;
	}
	public static StringBuilder toString(char [] arr,int l,int r) {
		StringBuilder sb=new StringBuilder();
		for(int i=l;i<=r;i++) sb.append(arr[i]);
		return sb;
	}
	static class InputReader  {
		 
		private InputStream in;
		private byte[] buffer = new byte[1024];
		private int curbuf;
		private int lenbuf;
 
		public InputReader(InputStream in) {
			this.in = in;
			this.curbuf = this.lenbuf = 0;
		}
 
		public boolean hasNextByte() {
			if (curbuf >= lenbuf) {
				curbuf = 0;
				try {
					lenbuf = in.read(buffer);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return false;
			}
			return true;
		}
 
		private int readByte() {
			if (hasNextByte())
				return buffer[curbuf++];
			else
				return -1;
		}
 
		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}
 
		private void skip() {
			while (hasNextByte() && isSpaceChar(buffer[curbuf]))
				curbuf++;
		}
 
		public boolean hasNext() {
			skip();
			return hasNextByte();
		}
 
		public String next() {
			if (!hasNext())
				throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (!isSpaceChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
 
		public int nextInt() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}
 
		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}
 
		public double nextDouble() {
			return Double.parseDouble(next());
		}
 
		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 char[][] nextCharMap(int n, int m) {
			char[][] map = new char[n][m];
			for (int i = 0; i < n; i++)
				map[i] = next().toCharArray();
			return map;
		}
	}

	}