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.*;
     
public class Solution {

    public static void main(String[] args) throws Exception{ 
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
        int t = Integer.parseInt(br.readLine());
        
        while(t > 0){
             String w = br.readLine(); 
             int x = Integer.parseInt(br.readLine());
             
             boolean[] index = new boolean[w.length()];
             boolean possible = true;
             for(int i=0;i<w.length();i++){
                  if(w.charAt(i) == '0'){
                       if(i>=x){
                            index[i-x] = true;
                       }
                       if(i+x < w.length()){
                           index[i+x] = true;
                       }
                  }
             }
             
             for(int i=0; i<w.length();i++){
                  if(w.charAt(i) == '1'){
                      if(i>=x && i+x < w.length()){
                           if(index[i-x] && index[i+x]){
                                possible =false;
                                break;
                           } 
                       }
                       else if(i>=x){
                            if(index[i-x]){
                                 possible = false;
                                 break;
                            }
                       }
                       
                       else if(i+x < w.length()){
                           if(index[i+x]){
                                 possible =false;
                                 break;
                            } 
                       } 
                       else{
                           possible =false;
                          break; 
                       }
                  }
             }
             if(possible){
                  StringBuilder sb = new StringBuilder();
                  for(int i=0;i<w.length();i++){
                       if(index[i])
                         sb.append(0);
                       else
                         sb.append(1);
                  }
                   out.println(sb.toString()); 
             }
             else{
                  out.println(-1);
             }
             t--;
        }
        out.close();
    }
}