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.
/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

import java.io.BufferedReader;
import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.LinkedList;
import java.util.Queue;
import java.util.StringTokenizer;

/**
 *
 * @author is2ac
 */
public class D_CF {

    public static void main(String[] args) throws IOException {
        FastScanner58 fs = new FastScanner58();
        //Reader fs = new Reader();
        PrintWriter pw = new PrintWriter(System.out);
        int t = fs.ni();
        //int t = 1;
        for (int tc = 0; tc < t; tc++) {
           int n = fs.ni();
           long k = fs.nl();
           String s = fs.next();
           int[] ch = new int[n];
           Queue<Long> q = new LinkedList();
           for (int i = 0; i < ch.length; i++) {
               if (s.charAt(i)=='0') {
                   q.add((long)i);
               } else {
                   ch[i] = 1;
               }
           }
           long ind = 0;
           while (!q.isEmpty() && k>0) {
               long j = q.poll();
               ch[(int)j] = 1;
               if (j-ind>k) {
                ch[(int)(j-k)] = 0;
                k = 0;
               } else {
                ch[(int)ind] = 0;
                k -= j-ind;   
               }
               ind++;
           }
           StringBuilder sb = new StringBuilder();
           for (int i = 0; i < n; i++) {
               sb.append(ch[i]);
           }
           pw.println(sb);
        }
        pw.close();
    }
    public static long gcd(long n1, long n2) {
        if (n2 == 0) {
            return n1;
        }
        return gcd(n2, n1 % n2);
    }
}
class BIT16 {
    int[] bit;
    public BIT16(int size) {
        bit = new int[size];
    }
    public void update(int ind, int delta) {
        while (ind<bit.length) {
            bit[ind]+=delta;
            ind = ind + (ind&(-1*ind));
        }
    }
    public int sum(int ind) {
        int s = 0;
        while (ind>0) {
            s += bit[ind];
            ind = ind - (ind&(-1 * ind));
        }
        return s;
    }
    public int query(int l, int r) {
        return sum(r)-sum(l);
    }
}
class UnionFind18 {

    int[] id;

    public UnionFind18(int size) {
        id = new int[size];
        for (int i = 0; i < size; i++) {
            id[i] = i;
        }
    }

    public int find(int p) {
        int root = p;
        while (root != id[root]) {
            root = id[root];
        }
        while (p != root) {
            int next = id[p];
            id[p] = root;
            p = next;
        }
        return root;
    }

    public void union(int p, int q) {
        int a = find(p), b = find(q);
        if (a == b) {
            return;
        }
        id[b] = a;
    }
}
class Reader
    {
        final private int BUFFER_SIZE = 1 << 16;private DataInputStream din;private byte[] buffer;private int bufferPointer, bytesRead;
        public Reader(){din=new DataInputStream(System.in);buffer=new byte[BUFFER_SIZE];bufferPointer=bytesRead=0;
        }public Reader(String file_name) throws IOException{din=new DataInputStream(new FileInputStream(file_name));buffer=new byte[BUFFER_SIZE];bufferPointer=bytesRead=0;
        }public String readLine() throws IOException{byte[] buf=new byte[64];int cnt=0,c;while((c=read())!=-1){if(c=='\n')break;buf[cnt++]=(byte)c;}return new String(buf,0,cnt);
        }public int ni() throws IOException{int ret=0;byte c=read();while(c<=' ')c=read();boolean neg=(c=='-');if(neg)c=read();do{ret=ret*10+c-'0';}while((c=read())>='0'&&c<='9');if(neg)return -ret;return ret;
        }public long nextLong() throws IOException{long ret=0;byte c=read();while(c<=' ')c=read();boolean neg=(c=='-');if(neg)c=read();do{ret=ret*10+c-'0';}while((c=read())>='0'&&c<='9');if(neg)return -ret;return ret;
        }public double nextDouble() throws IOException{double ret=0,div=1;byte c=read();while(c<=' ')c=read();boolean neg=(c=='-');if(neg)c = read();do {ret=ret*10+c-'0';}while((c=read())>='0'&&c<='9');if(c=='.')while((c=read())>='0'&&c<='9')ret+=(c-'0')/(div*=10);if(neg)return -ret;return ret;
        }private void fillBuffer() throws IOException{bytesRead=din.read(buffer,bufferPointer=0,BUFFER_SIZE);if(bytesRead==-1)buffer[0]=-1;
        }private byte read() throws IOException{if(bufferPointer==bytesRead)fillBuffer();return buffer[bufferPointer++];
        }public void close() throws IOException{if(din==null) return;din.close();}
    }
class FastScanner58 {

    BufferedReader br;
    StringTokenizer st;

    public FastScanner58() {
        br = new BufferedReader(new InputStreamReader(System.in), 32768);
        st = null;
    }

    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

    int ni() {
        return Integer.parseInt(next());
    }

    int[] intArray(int N) {
        int[] ret = new int[N];
        for (int i = 0; i < N; i++) {
            ret[i] = ni();
        }
        return ret;
    }

    long nl() {
        return Long.parseLong(next());
    }

    long[] longArray(int N) {
        long[] ret = new long[N];
        for (int i = 0; i < N; i++) {
            ret[i] = nl();
        }
        return ret;
    }

    double nd() {
        return Double.parseDouble(next());
    }

    String nextLine() {
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }
}

