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.*;

public class MyClass {
    public static void main(String args[]) {
      
        Scanner sc = new Scanner(System.in);
      
        int tests = sc.nextInt();
      
        for(int t=0; t<tests; t++){
            
            String str = sc.next();
            int x = sc.nextInt();
            char[] ans = new char[str.length()];
            for(int i=0; i<str.length(); i++){
                ans[i]='1';
            }
            for(int i=0; i<str.length(); i++){
                if(str.charAt(i)=='0'){
                    if(i-x>=0){
                        ans[i-x]='0';
                    }
                    if(i+x<ans.length){
                        ans[i+x]='0';
                    }
                }
            }
            //System.out.println(res);
            boolean flag = true;
            String res = "";
            for(int i=0; i<str.length(); i++){
                if(str.charAt(i)=='1'){
                    if((i-x<0 || ans[i-x]=='0') && (i+x>=ans.length || ans[i+x]=='0') ){
                        System.out.println(-1);
                        flag=false;
                        break;
                    }
                }
                res+=ans[i];
            }
            if(flag){
                System.out.println(res);
            }
        }
    }
}