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.io.*;import java.math.*;

public class Main
{
    static void swap(int i,int j,int arr[]){
        int t=arr[j];
        arr[j]=arr[i];
        arr[i]=t;
    }

    public static void process()throws IOException
    {
        int n=ni(),arr[]=new int[n+1],lt=1;
        long k=nl();
        String xyz=" "+nln();

        for(int i=1;i<=n;i++) arr[i]=xyz.charAt(i)-'0';

        for(int i=1;i<=n;i++){
            if(k==0)
                break;
            if(arr[i]==1)
                continue;

            //when arr[i]=0
            int sw=0,can_go=0;
            
            if(i-lt<=k)
                can_go=lt;
            else
                can_go=(int)(i-k);
            //can_go=Math.min(i-lt, i-k);
            if(can_go<1)
                can_go=lt;
            swap(i,can_go,arr);
            k-=(i-can_go);
            if(can_go==lt)
                lt++;

            if(lt>=n)
                break;
        }

        for(int i=1;i<=n;i++) p(arr[i]);
        pn("");
    }


   	static AnotherReader sc;
    static PrintWriter out;
    public static void main(String[]args)throws IOException
    {
        out = new PrintWriter(System.out);
        sc=new AnotherReader();
        boolean oj = true;

    	oj = System.getProperty("ONLINE_JUDGE") != null;
    	if(!oj) sc=new AnotherReader(100);

        long s = System.currentTimeMillis();
        int t=ni();
        while(t-->0)
            process();
        out.flush();
        if(!oj)
            System.out.println(System.currentTimeMillis()-s+"ms");
        System.out.close();  
    }

    static void pn(Object o){out.println(o);}
    static void p(Object o){out.print(o);}
    static void pni(Object o){out.println(o);System.out.flush();}
    static int ni()throws IOException{return sc.nextInt();}
    static long nl()throws IOException{return sc.nextLong();}
    static double nd()throws IOException{return sc.nextDouble();}
    static String nln()throws IOException{return sc.nextLine();}
    static long gcd(long a, long b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int gcd(int a, int b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int bit(long n)throws IOException{return (n==0)?0:(1+bit(n&(n-1)));}
    static boolean multipleTC=false;



/////////////////////////////////////////////////////////////////////////////////////////////////////////

    static class AnotherReader{BufferedReader br; StringTokenizer st;
    AnotherReader()throws FileNotFoundException{
    br=new BufferedReader(new InputStreamReader(System.in));}
    AnotherReader(int a)throws FileNotFoundException{
    br = new BufferedReader(new FileReader("input.txt"));}
    String next()throws IOException{
    while (st == null || !st.hasMoreElements()) {try{
    st = new StringTokenizer(br.readLine());}
    catch (IOException  e){ e.printStackTrace(); }}
    return st.nextToken(); } int nextInt() throws IOException{
    return Integer.parseInt(next());}
    long nextLong() throws IOException
    {return Long.parseLong(next());}
    double nextDouble()throws IOException { return Double.parseDouble(next()); }
    String nextLine() throws IOException{ String str = ""; try{
    str = br.readLine();} catch (IOException e){
    e.printStackTrace();} return str;}}
    
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
}
	
	
	