Consider the following process. You have a binary string (a string where each character is either 0 or 1) w of length n and an integer x. You build a new binary string s consisting of n characters. The i-th character of s is chosen as follows:

  * if the character w_{i-x} exists and is equal to 1, then s_i is 1 (formally, if i > x and w_{i-x} =  1, then s_i =  1); 
  * if the character w_{i+x} exists and is equal to 1, then s_i is 1 (formally, if i + x ≤ n and w_{i+x} =  1, then s_i =  1); 
  * if both of the aforementioned conditions are false, then s_i is 0. 



You are given the integer x and the resulting string s. Reconstruct the original string w.

Input

The first line contains one integer t (1 ≤ t ≤ 1000) — the number of test cases.

Each test case consists of two lines. The first line contains the resulting string s (2 ≤ |s| ≤ 10^5, each character of s is either 0 or 1). The second line contains one integer x (1 ≤ x ≤ |s| - 1).

The total length of all strings s in the input does not exceed 10^5.

Output

For each test case, print the answer on a separate line as follows:

  * if no string w can produce the string s at the end of the process, print -1; 
  * otherwise, print the binary string w consisting of |s| characters. If there are multiple answers, print any of them. 

Example

Input


3
101110
2
01
1
110
1


Output


111011
10
-1
import java.io.*;
import java.util.*;
import java.util.Arrays.*;
public class Binary
{
    public static void main(String[] args) throws IOException
    {
        Scanner in=new Scanner(System.in);
        PrintWriter out=new PrintWriter(System.out);
        int t=in.nextInt();
        while(t-->0)
        {
             in.nextLine();
            String s=in.nextLine();
            int x=in.nextInt();
            int n=s.length();       
            int w[]=new int[n];
            for(int j=0;j<n;j++)
            
                w[j]=1;
            for(int k=0;k<n;k++)
                {
                    if(s.charAt(k)=='0')
                    {
                        if(k>=x)
                    w[k-x]=0;
                    if(k+x<n)
                    w[k+x]=0;
                   }
                }
                    
                int fl=0;
           for(int i=0;i<n;i++)
           {
               if(s.charAt(i)=='1')
               {
                int f=0;
               if((i>=x) && (w[i-x]==1))
               {
                  f=1;
               }
               if(i+x<n && w[i+x]==1)
                {
                    f=1;
                }
               if(f==0)
                   {
                    fl=1;
                    break;
                   }
                }
           } 
          if(fl==1)
          {
           out.print("-1");
          }
          else
          {
              
              for(int i=0;i<n;i++)
              {
                out.print(w[i]);
              }
          }
          out.println();
}
    out.close();
}
            
}