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
// Don't place your source in a package
import java.util.*;
import java.lang.*;
import java.io.*;
import java.math.*;






// Please name your class Main
public class Main {
    static Scanner in = new Scanner(System.in);
    public static void main (String[] args) throws java.lang.Exception {
        PrintWriter out = new PrintWriter(System.out);

        int T=Int();
        for(int t=0;t<T;t++){
            String s=Str();
            int x=Int();
            Solution sol=new Solution();
            sol.solution(out,s,x);

        }
        out.flush();

    }

    public static long Long(){
        return in.nextLong();
    }
    public static int Int(){
        return in.nextInt();
    }
    public static String Str(){
        return in.next();
    }
}


class Solution{

    public void solution(PrintWriter out,String s,int x){
        int n=s.length();
        char A[]=new char[n];
        Arrays.fill(A,'1');


        for(int i=0;i<s.length();i++){
            char c=s.charAt(i);
            if(c=='0'){
                if(i+x<A.length){
                    A[i+x]='0';
                }
                if(i-x>=0){
                    A[i-x]='0';
                }

            }
        }
        


        for(int i=0;i<s.length();i++){
            char c=s.charAt(i);
            if(c=='1'){
                boolean good=false;
                if(i+x<A.length&&A[i+x]=='1'){
                    good=true;
                }
                if(i-x>=0&&A[i-x]=='1'){
                    good=true;
                }

                if(!good){
                    System.out.println(-1);
                    return;
                }
            }
        }



        String res=new String(A);
        System.out.println(res);
    }





}

