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
/*
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 * and open the template in the editor.
 */

/**
 *
 * @author Hp
 */
import java.io.*;
import java.util.*;
public class ProblemC {
    public static void main(String args[])throws IOException{
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        while(t > 0){
            String s = sc.next();
            int x = sc.nextInt();
            int n = s.length();
            
            char arr[] = s.toCharArray();
            char ans[] = new char[n];
            for(int i = 0; i < n;i++)
                ans[i] = '1';
            
            //w construction
            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';
                }
            }
            
            //checking w
            int fl = 0;
            for(int i = 0; i < n;i++){
                char val = '0';
                if(i - x >= 0){
                    if(ans[i-x] == '1')
                        val = '1';
                }
                if(i + x < n){
                    if(ans[i + x] == '1')
                        val = '1';
                }
                if(val != arr[i]){
                    fl = 1;
                    break;
                }    
            }
            
            if(fl == 0)
                System.out.println(new String(ans));
            else
                System.out.println(-1);
            t--;
        }
    }
}