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


//Mann Shah [ DAIICT ].
//fast io

public class Main {
	public static int mod = (int) (1e9 + 7);
	public static long inf = (long) 1e15 + 42;
	static InputReader in;
	static PrintWriter out;

	public static long gcd(long a, long b) {
		if (a == 0)
			return b;
		return gcd(b % a, a);
	}
	
	
	public static void main(String args[]) {

		in = new InputReader(System.in);
		out = new PrintWriter(System.out);
		
		int q = in.nextInt();
		while(q-->0) {
			int n = in.nextInt();
			long k = in.nextLong();
			char[] s = in.readString().toCharArray();
			
			int values[] = new int[n];
            Arrays.fill(values, -1);
            int ones = 0;
            for (int i = 0; i < n; ++i) {
                if (s[i] == '1')
                    ones++;
                else {
                    long poss = Math.min(ones, k);
                    k -= (int) poss;
                    values[i - (int) poss] = 0;
                }
            }
            for (int i = 0; i < n; ++i) {
                out.print(values[i] == 0 ? 0 : 1);
            }
            out.println();
		}
		
		
		out.close();
	}

	static class InputReader {

		private final InputStream stream;
		private final byte[] buf = new byte[8192];
		private int curChar, snumChars;
		private SpaceCharFilter filter;

		public InputReader(InputStream stream) {
			this.stream = stream;
		}

		public int snext() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public int nextInt() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public long nextLong() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		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 String readString() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public String nextLine() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isEndOfLine(c));
			return res.toString();
		}

		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}

	}

}

// For Pair sorting

// Arrays.sort(arr,new Comparator<Pair>() {
// @Override public int compare(Pair p1, Pair p2)
// {
// return p1.x - p2.x;
// }
// });

class Pair {
	int x;
	int y;

	// Constructor
	public Pair(int x, int y) {
		this.x = x;
		this.y = y;
	}
	
	@Override
	public boolean equals(Object o) {
		Pair p =(Pair)o;
		return (x==p.x && y==p.y);
	}
}

class x{
	//declare variables
	int abc;
	
	//constructor
	public x(int abc) {
		this.abc = abc;
	}
	
}


class couple implements Comparable<couple> {
	int x, y;

	public couple(int m, int f) {
		x = m;
		y = f;
	}

	public int compareTo(couple o) {

		return x - o.x;
	}
}