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.
//package learning;
import java.util.*;
import java.io.*;
import java.lang.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;
public class NitsLocal {
    static ArrayList<String> s1;
    static boolean[] prime;
    static int n = (int)1e7;
    
     static void sieve() {
Arrays.fill(prime	, true);
prime[0] = prime[1] = false;
for(int i = 2 ; i * i <= n ; ++i) {
if(prime[i]) {
for(int k = i * i; k<= n ; k+=i) {
prime[k] = false;
}
}
}
 
}
    public static void main(String[] args) {
        InputReader sc = new InputReader(System.in);
        
           prime  = new boolean[n + 1];
           //sieve();
                prime[1] = false;
                /*
              int n = sc.ni();     
              int []a = sc.nia(n);
              int mod = 1000000007;
              long ans = 0;
              int f = 0;
              int q = sc.ni();
              while(q-- > 0)
              {
                  int num = sc.ni();
                  ans = 0;
                  if(num == 0)
                  {
                      a[sc.ni()-1] = sc.ni();
                  }
                 else
                  {
                      int l = sc.ni();
                      int r = sc.ni();
                    for(int i=l-1;i<r;i++)
                   {
                  
                   for(int j=i+1;j<r;j++)
                   {
                      f = 0;
                   
                      int x = a[i];
                      int y = a[j];
                      while(x > 0 && y > 0)
                      {
                          int y1 = x%10;
                          int y2 = y%10;
                          if(y1 > 0 && y2 > 0)
                          {
                              f = 1;
                          }
                          x /= 10;
                          y /= 10;
                      }
                      
                    
                    
                   
                     if(f==0)
                     {
                         ans = (ans + ((((long)a[i]%mod) * ((long)a[j]%mod)))%mod)%mod;
                     }
                  }
              }
              
              w.println(ans);
                  }
              }
          
            */
               
                   
              
                int q  =sc.ni();
                while(q-- > 0)
                {
                   int n = sc.ni();
                   long k = sc.nl();
                   long c = 0;
                   ArrayList<Integer> res = new ArrayList<>();
                   int []up = new int[n+1];
                   char []ch = sc.rs().toCharArray();
                   int j = 0;
                   for(int i=0;i<n;i++)
                   {
                       if(ch[i] == '0')
                       {
                           res.add(i+1);
                           up[j] = i+1; 
                           j++;
                       }
                   }
                   for(int i=0;i<res.size();i++)
                   {
                       int req = res.get(i)-i-1;
                       if(k >= req)
                       {
                           k -= req;
                           up[i] = i+1;
                       }
                       else
                       {
                           up[i] = res.get(i)-(int)k;
                           k = 0;
                           break;
                       }
                   }
                   char []r1 = new char[n];
                   for(int i=0;i<n;i++)
                   {
                       r1[i] = '1';
                   }
                   for(int i=0;i<res.size();i++)
                   {
                       r1[up[i] - 1] = '0';
                   }
                   for(int i=0;i<n;i++)
                   {
                       w.print(r1[i]);
                   }
                  w.println();
                }
             
      
       w.close();
       
        
    }
    public static int countSetBits(int number){
        int count = 0;
        while(number>0){
            ++count;
            number &= number-1;
        }
        return count;
    }
    /*
     static  class CustomerSortingComparator 
                                implements Comparator<Temp> {
 
    @Override
    public int compare(Temp cust1, Temp cust2) {
 
        // all comparison
        int compareName = 0;
        if(cust1.a < cust2.a)
            compareName= -1;
        
        else if(cust1.a > cust2.a)
        compareName = 1;
        else
            compareName = 0;
        int compareCity = 0;
        if(cust1.b < cust2.b)
            compareCity = -1;
        
        else if(cust1.b > cust2.b)
        compareCity  = 1;
        else
            compareCity  = 0;
        int compareAge = 0;
        if(cust1.d < cust2.d)
            compareAge  = -1;
        
        else if(cust1.d > cust2.d)
        compareAge  = 1;
        else
            compareAge  = 0;
 
        // 3-level comparison using if-else block
        if(compareName == 0) {
            return ((compareCity == 0) ? compareAge : compareCity);
        }
        else {
            return compareName;
        }
    }
    }
*/
    public static long pow(long i, long j) {
		long res=1L;
		for(int a=0;a<j;a++) res*=i;
		return res;
	}
    public static long powmod(long i, long j,long MOD) {
		if(j==0) return 1L;
		if(j%2==0) {
			long temp=powmod(i,j/2,MOD);
			return (temp*temp)%MOD;
		}
		return (i*powmod(i,j-1,MOD))%MOD;
	}
    static HashSet<Integer> fac;
    public static void primeFactors(int n) 
    { 
        // Print the number of 2s that divide n 
        int t = 0;
        while (n%2==0) 
        { 
            fac.add(2);
            n /= 2; 
        } 
  
        // n must be odd at this point.  So we can 
        // skip one element (Note i = i +2) 
        for (int i = 3; i*i <= n; i+= 2) 
        { 
            // While i divides n, print i and divide n 
            while (n%i == 0) 
            { 
                fac.add(i);
                n /= i; 
            } 
        } 
  
        // This condition is to handle the case whien 
        // n is a prime number greater than 2 
        if (n > 2) 
            fac.add(n);
    } 
     static long modexp(long x,long n,long M)
{
    long power = n;
    long result=1;
    x = x%M;
    while(power>0)
    {
        if(power % 2 ==1)
            result=(result * x)%M;
        x=(x*x)%M;
        power = power/2;
    }
    return result;
}
    static int gcd(int a,int b)
    {
        if(a==0)
            return b;
        else
            return gcd(b%a,a);
    }
    static class Temp{
        int a;
        int b;
      
        Temp(int a,int b)
        {
            this.a = a;
            this.b = b;
            //this.d = d;
        }
    }
    static class Query{
        int p;
        int index;
        int value;
        public Query(int p,int index,int value)
        {
            this.p = p;
            this.index = index;
            this.value = value;
            
        }
    }
    static int nextPowerOf2(int n) 
    { 
        int count = 0; 
  
        // First n in the below  
        // condition is for the  
        // case where n is 0 
        if (n > 0 && (n & (n - 1)) == 0) 
            return n; 
  
        while(n != 0) 
        { 
            n >>= 1; 
            count += 1; 
        } 
  
        return 1 << count; 
    } 
    
   static long sum1(int t1,int t2,int x,int []t)
   {
       int mid = (t2-t1+1)/2;
  if(t1==t2)
      return 0;
    
   else
   return sum1(t1,mid-1,x,t) + sum1(mid,t2,x,t);
    
     
   }
  
   
    static String replace(String s,int a,int n)
    {
        char []c = s.toCharArray();
        for(int i=1;i<n;i+=2)
        {
            int num = (int) (c[i] - 48);
            num += a;
            num%=10;
            c[i] = (char) (num+48);
        }
        return new String(c);
    }
    static String move(String s,int h,int n)
    {
        h%=n;
        char []c = s.toCharArray();
        char []temp = new char[n];
        for(int i=0;i<n;i++)
        {
            temp[(i+h)%n] = c[i];
        }
        return new String(temp);
    }
    
     public static int ip(String s){
return Integer.parseInt(s);
}
     static class multipliers implements Comparator<Long>{
  
         
  public int compare(Long a,Long b) {
   if(a<b)
    return 1;
   else if(b<a)
    return -1;
   else
    return 0;
  }
 }
     static class multipliers1 implements Comparator<Student>{
  
  public int compare(Student a,Student b) {
   if(a.y<b.y)
    return 1;
   else if(b.y<a.y)
    return -1;
   else
   {
       if(a.id < b.id)
           return 1;
       else if(b.id<a.id)
           return -1;
       else
           return 0;
           
    //return 0;
   }
  }
 }
    // Java program to generate power set in 
// lexicographic order. 
 
    
    
    
      static class InputReader {
 
private final InputStream stream;
private final byte[] buf = new byte[8192];
private int curChar, snumChars;
 
public InputReader(InputStream st) {
this.stream = st;
}
 
public int read() {
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 ni() {
int c = read();
while (isSpaceChar(c)) {
c = read();
}
int sgn = 1;
if (c == '-') {
sgn = -1;
c = read();
}
int res = 0;
do {
res *= 10;
res += c - '0';
c = read();
} while (!isSpaceChar(c));
return res * sgn;
}
 
public long nl() {
int c = read();
while (isSpaceChar(c)) {
c = read();
}
int sgn = 1;
if (c == '-') {
sgn = -1;
c = read();
}
long res = 0;
do {
res *= 10;
res += c - '0';
c = read();
} while (!isSpaceChar(c));
return res * sgn;
}
 
public int[] nia(int n) {
int a[] = new int[n];
for (int i = 0; i < n; i++) {
a[i] = ni();
}
return a;
}
 
public String rs() {
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 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 boolean isSpaceChar(int c) {
return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
}
 
private boolean isEndOfLine(int c) {
return c == '\n' || c == '\r' || c == -1;
}
 
}
 
 
 
 
 
   
static PrintWriter w = new PrintWriter(System.out);
                  static class Student
    {
        int id;
        //int x;
       
        int y;
        //long z;
        
        Student(int id,int y)
        {
            this.id = id;
            //this.x = x;
            //this.s = s;
            this.y = y;
           // this.z = z;
            
            
            
        }
        
    }
}