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 javax.lang.model.util.ElementScanner6;

import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class q3
{
	public static void main (String[] args) throws java.lang.Exception
	{
        // your code goes here
        Scanner sc = new Scanner(System.in);
        int t= Integer.parseInt(sc.next());
        while(t-->0)
        { 
            String s= sc.next();
            int n= s.length();
            int x= Integer.parseInt(sc.next());
            char[] ans= new char[n];
            Arrays.fill(ans,'1');
            char[] arr = s.toCharArray();
            int f2=0;
            for(int i=0;i<n;i++)
            {
                if(arr[i]=='0')
                {
                    if(i-x>=0)
                    {
                        ans[i-x]='0';
                    }
                    if(i+x<n)
                    {
                        ans[i+x]='0';
                    }
                }
            }
            for(int i=0;i<n;i++)
            {
                int flag=0;
                int rf=0;
                if(arr[i]=='1')
                {
                   
                    if(i-x>=0)
                    { 
                        
                        if(ans[i-x]=='1')
                        {
                            flag=1;
                        }

                    }
                    if(i+x<n)
                    {
                       if(ans[i+x]=='1')
                        {
                            rf=1;
                        }
                    }
                    if(flag==0 && rf==0)
                    {
                        System.out.println(-1);
                        f2=1;
                        break;
                    }
                }
            }
            if(f2==1)
            {
                continue;
            }
            System.out.println(String.valueOf(ans));
          
        
          
        }
    }
}