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.

//When I wrote this code, only God & I understood what it did. Now only God knows !!


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


public class Main {

    static class FastReader
    {
        private InputStream mIs;private byte[] buf = new byte[1024];private int curChar,numChars;public FastReader() { this(System.in); }public FastReader(InputStream is) { mIs = is;}
        public int read() {if (numChars == -1) throw new InputMismatchException();if (curChar >= numChars) {curChar = 0;try { numChars = mIs.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 next(){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 l(){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 i(){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 double d() throws IOException {return Double.parseDouble(next()) ;}
        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; }
        public void scanIntArr(int [] arr){ for(int li=0;li<arr.length;++li){ arr[li]=i();}}
        public void scanLongArr(long [] arr){for (int i=0;i<arr.length;++i){arr[i]=l();}}
        public void shuffle(int [] arr){ for(int i=arr.length;i>0;--i) { int r=(int)(Math.random()*i); int temp=arr[i-1]; arr[i-1]=arr[r]; arr[r]=temp; } }
    }

    public static void main(String[] args) throws IOException {

        FastReader fr = new FastReader();
        PrintWriter pw = new PrintWriter(System.out);
        /*
inputCopy
3
8 5
11011010
7 9
1111100
7 11
1111100
outputCopy
01011110
0101111
0011111

        */
        int q=fr.i();
        for(int qi=0;qi<q;++qi)
        {
            int n=fr.i();
            long totalMoves=fr.l();
            char [] arr=fr.nextLine().toCharArray();
            long curMoves=0;
            int totalZereos=0;
            boolean flag=false;
            int i;
            for(i=0;i<arr.length;++i)
            {
                if(arr[i]=='0')
                {
                    curMoves+=(i-totalZereos);
                    if(curMoves>totalMoves)
                    {
                        curMoves-=(i-totalZereos);
                        break;
                    }
                    ++totalZereos;
                }
            }
            char [] ans=new char[n];
            for(int i2=0;i2<totalZereos;++i2)
                ans[i2]='0';
            for(int i2=totalZereos;i2<i;++i2)
            {
                ans[i2]='1';
            }
            for(int i2=i;i2<n;++i2)
            {
                ans[i2]=arr[i2];
            }
            long remMoves=totalMoves-curMoves;
            while(remMoves>0 && i<n && i>0)
            {
                swap(ans,i,i-1);
                --remMoves;
                --i;
            }
            pw.println(String.valueOf(ans));
        }
        pw.flush();
        pw.close();
    }
    public static void swap(char [] arr,int i,int j)
    {
        char temp=arr[i];
        arr[i]=arr[j];
        arr[j]=temp;
    }
}
