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.
import java.util.*;

import java.awt.Point;
import java.io.*;
import java.math.BigInteger;
public class Solutions {
	 
	static FastScanner scr=new FastScanner();
	static PrintStream out=new PrintStream(System.out);
//	static ArrayList<ArrayList<Integer>>list=new ArrayList<ArrayList<Integer>>();
	public static void main(String []args) {
		int t=scr.nextInt();
		while(t-->0) {
			solve();
		}
	}
	static void solve() {
		int n=scr.nextInt();
		long k=scr.nextLong();
		char c[]=scr.next().toCharArray();
		ArrayList<Integer>a=new ArrayList<Integer>();
		int zeroCount=0;
		char ans[]=new char[n];
		Arrays.fill(ans,'1');
		for(int i=0;i<n;i++) {
			if(c[i]=='0') {
				int shift=(int)Math.min(i-zeroCount,k);
				k-=shift;
				ans[i-shift]='0';
				zeroCount++;
			}
		}
		String s=new String(ans);
		out.println(s);
	}
	static void swap(int a[],int i,int j) {
		int temp=a[i];a[i]=a[j];
		a[j]=temp;
	}
	static long modPow(long base,long exp,long mod) {
		if(exp==0) {
			return 1;
		}
		if(exp%2==0) {
			long res=(modPow(base,exp/2,mod));
			return (res*res)%mod;
		}
		return (base*modPow(base,exp-1,mod))%mod;
	}
	static long parse(String s) {
		return Long.parseLong(s);
	}
	static boolean count(int n) {
		if(n<2) {
			return false;
		}
		for(int i=2;i*i<=n;i++) {
			if(n%i==0) {
				return false;
			}
		}
		return true;
	}
	static boolean check(int a[],int b[],int x,int y) {
		for(int i=0;i<a.length;i++) {
			if(a[i]!=x && a[i]!=y && b[i]!=x && b[i]!=y) {
				return false;
			}
		}
		return true;
	}
	static int gcd(int a,int b) {
		if(b==0) {
			return a;
		}
		return gcd(b,a%b);
	}
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long[] readLongArray(int n) {
			long  [] a=new long  [n];
			for (int i=0; i<n; i++) a[i]=nextLong();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}
	static int MAX=Integer.MAX_VALUE;
	static int MIN=Integer.MIN_VALUE;
}class triplet{
	int x;
	int y;
	int z;
	triplet(int fisrt,int second,int third){
		this.x=fisrt;
		this.y=second;
		this.z=third;
	}
}
class pair{
	int x=0;
	int y=0;
	pair(int first,int second){
		this.x=first;
		this.y=second;
	}
}