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.util.*;
import java.io.*;
public class Solution{
    public static void main(String args[])throws IOException
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bw=new BufferedWriter(new OutputStreamWriter(System.out));
        int t=Integer.parseInt(br.readLine());
        while(t-->0)
        {
          
          char ch[]=br.readLine().toCharArray();
          int k=Integer.parseInt(br.readLine());
          char ans[]=new char[ch.length];
          for(int i=0;i<ch.length;i++)
          ans[i]='#';
          
          boolean flag=true;
          
          for(int i=0;i<k;i++)
          {
              if(ch[i]=='1')
              {
                  if(i+k>=ch.length)
                  flag=false;
                  else
                  ans[i+k]='1';
              }
              
              else
              {
                  if(i+k<ch.length)
                  ans[i+k]='0';
              }
          }
          
           for(int i=ch.length-1;(i+k)>=ch.length;i--)
          {
              if(ch[i]=='1')
              {
                  if(i-k<0)
                  flag=false;
                  else
                  {
                      if(ans[i-k]!='0')
                       ans[i-k]='1';
                       else
                       flag=false;
                      
                  }
                 
              }
              
              else
              {
                
                  if(i-k>=0&&ans[i-k]=='1')
                  flag=false;
                  else
                  {
                      if(i-k>=0)
                       ans[i-k]='0';
                  }
                 
              }
          }
          
          for(int i=k;(i+k)<ch.length;i++)
          {
              if(ch[i]=='1')
              {
                 
                  
                  if(ans[i-k]=='0'&&ans[i+k]=='0')
                  flag=false;
                  
                  if(ans[i-k]=='#'||ans[i-k]=='1')
                  ans[i-k]='1';
                  else
                  {
                      if(ans[i+k]=='#'||ans[i+k]=='1')
                      ans[i+k]='1';
                      else
                      flag=false;
                      
                      
                  }
                  
                
              }
              else
              {
                  if(ans[i-k]=='#')
                  ans[i-k]='0';
                  if(ans[i+k]=='#')
                  ans[i+k]='0';
                  
                  if(ans[i+k]!='0'||ans[i-k]!='0')
                  flag=false;
                  
              }
          }
          
          for(int i=0;i<ch.length;i++)
          {
              if(ans[i]=='#')
              ans[i]='1';
          }
          
        
          
          if(flag)
          {
              String mystr=new String(ans);
              bw.write(mystr+"\n");
          }
          else
          {
              bw.write("-1\n");
          }
          
          
        }
        bw.close();
    }
}