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.*;
 
 
// BufferedReader br = new BufferedReader(new InputStreamreader(System.in));
// StringTokenizer st = new StringTokenizer(br.readLine());
// Integer.parseInt(st.nextToken());
// Integer.parseInt(br.readLine());
 
public class MyClass {
    public static void main(String args[]) throws IOException{
      BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    // Scanner sc = new Scanner(System.in);
      int t =  Integer.parseInt(br.readLine());
      while(t-->0){
          String s = br.readLine();
          int x = Integer.parseInt(br.readLine());
          int n = s.length();
          char[] carr = new char[n];
          Arrays.fill(carr,'a');
          for(int i =0;i<n;i++){
              if(i+x<n ){
                  if(s.charAt(i)=='0'){
                      carr[i+x]='0';
                  }
              }
              if(i-x>=0){
                  if(s.charAt(i)=='0'){
                      carr[i-x]='0';
                  }
              }
          }
          
        //   System.out.println(String.valueOf(carr));
          
          int flag=1;
          
          for(int i =0;i<n;i++){
              int f=0;
              if(s.charAt(i)=='0'){
                  f=1;
              }
              if(i+x<n){
                  if(s.charAt(i)=='1'){
                      if(carr[i+x]!='0'){
                          f=1;
                          carr[i+x]='1';
                      }
                      
                  }
                  
              }
              if(i-x>=0){
                  if(s.charAt(i)=='1'){
                      if(carr[i-x]!='0'){
                          f=1;
                          carr[i-x]='1';
                      }
                      
                  }
              }
              if(f==0){
                //   System.out.println(i+" "+s.charAt(i));
                  flag=0;
                  break;
              }
          }
          for(int i=0;i<n;i++){
              if(carr[i]=='a'){
                  carr[i]='1';
              }
          }
          if(flag==0){
              System.out.println(-1);
          }
          else{
            System.out.println(String.valueOf(carr));    
          }
          
      }
    }
}