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.*;
import java.util.*;
import java.awt.Point;
 
public class Main {
	//static final long MOD = 998244353;
	static final long MOD = 1000000007;
	static final int INF = 1000000007;
	
	public static void main(String[] args) {
		FastScanner sc = new FastScanner();
		int Q = sc.ni();
		StringBuilder ans = new StringBuilder();
		for (int q = 0; q < Q; q++) {
			int N = sc.ni();
			long K = sc.nl();
			String s = sc.next();
			ArrayList<Integer> zeros = new ArrayList<Integer>();
			for (int i = 0; i < N; i++) {
				if (s.charAt(i)=='0') {
					zeros.add(i);
				}
			}
			boolean[] num = new boolean[N];
			for (int i = 0; i < zeros.size(); i++) {
				if (K >= (zeros.get(i)-i)) {
					num[i] = true;
					K -= (zeros.get(i)-i);
				} else if (K > 0) {
					num[zeros.get(i)-((int)K)] = true;
					K = 0;
				}  else {
					num[zeros.get(i)] = true;
				}
			}
			StringBuilder queryAns = new StringBuilder();
			for (boolean n: num) {
				if (n)
					queryAns.append('0');
				else
					queryAns.append('1');
			}
			ans.append(queryAns + "\n");
		}
		System.out.print(ans);
 	}
	
	static class DisjointSetUnion {
		  public int[] parent;
		  public int[] rank;
		  public int count;
 
		  public DisjointSetUnion(int nodes) {
			  count = nodes;
			  parent = new int[nodes];
			  rank = new int[nodes];
			  for (int i = 0; i < nodes; i++) {
				  parent[i] = i;
				  rank[i] = 0;
			  }
		  }
		  //"find"
		  public int root(int p) {
			  if (parent[p] != p)
				  parent[p] = root(parent[p]);
			  return parent[p];
		  }
 
		  //"union"
		  public void connect(int p, int q) {
			  int rootP = root(p);
			  int rootQ = root(q);
			  if (rootP == rootQ) return;
			  if (rank[rootP] < rank[rootQ]) {
				  parent[rootP] = rootQ;
			  } else if (rank[rootP] > rank[rootQ]) {
				  parent[rootQ] = rootP;
			  } else {
				  parent[rootP] = rootQ;
				  rank[rootQ] += 1;
			  }
			  count--;
		  }
 
		  public boolean connected(int p, int q) {
		    return root(p) == root(q);
		  }
	}
    
    public static long power(long x, long y, long p) { 
        // Initialize result
        long res = 1;
         
        // Update x if it is more   
        // than or equal to p 
        x = x % p;  
      
        while (y > 0) 
        { 
            // If y is odd, multiply x 
            // with result 
            if((y & 1)==1) 
                res = (res * x) % p; 
      
            // y must be even now 
            // y = y / 2 
            y = y >> 1;  
            x = (x * x) % p;  
        } 
        return res; 
    }
    
    public static long dist(int[] point, int[] point2) {
    	return (long)(Math.pow((point2[1]-point[1]),2)+Math.pow((point2[0]-point[0]),2));
    }
    
    public static long gcd(long a, long b) {
    	if (b == 0)
    		return a;
    	else
    		return gcd(b,a%b);
    }
    
    public static int[][] sort(int[][] array) {
    	//Sort an array (immune to quicksort TLE)
		Random rgen = new Random();
		for (int i = 0; i < array.length; i++) {
		    int randomPosition = rgen.nextInt(array.length);
		    int[] temp = array[i];
		    array[i] = array[randomPosition];
		    array[randomPosition] = temp;
		}
		Arrays.sort(array, new Comparator<int[]>() {
			  @Override
        	  public int compare(int[] arr1, int[] arr2) {
				  return arr1[0]-arr2[0]; //ascending order
	          }
		});
		return array;
	}
    
    public static long[][] sort(long[][] array) {
    	//Sort an array (immune to quicksort TLE)
		Random rgen = new Random();
		for (int i = 0; i < array.length; i++) {
		    int randomPosition = rgen.nextInt(array.length);
		    long[] temp = array[i];
		    array[i] = array[randomPosition];
		    array[randomPosition] = temp;
		}
		Arrays.sort(array, new Comparator<long[]>() {
			  @Override
        	  public int compare(long[] arr1, long[] arr2) {
				  if (arr1[0] < arr2[0])
					  return -1;
				  if (arr1[0] > arr2[0])
					  return 1;
				  return 0;
	          }
		});
		return array;
	}
    
    static class FastScanner { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastScanner() { 
            br = new BufferedReader(new InputStreamReader(System.in)); 
        } 
  
        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()); 
        } 
  
        long nl() { 
            return Long.parseLong(next()); 
        } 
  
        double nd() { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() { 
            String str = ""; 
            try { 
                str = br.readLine(); 
            } catch (IOException e) {
                e.printStackTrace(); 
            } 
            return str; 
        }
    }
}