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.*;
public class Main
{
    public static void main(String args[])throws Exception
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw=new PrintWriter(System.out);
        int t=Integer.parseInt(br.readLine());
        while(t-->0)
        {
            char carr[]=br.readLine().toCharArray();
            char ans[]=new char[carr.length];
            Arrays.fill(ans,'1');
            int n=carr.length;
            int x=Integer.parseInt(br.readLine());
            for(int i=0;i<n;i++)
            {
                if(carr[i]=='0')
                {
                    if(i-x>=0)
                    ans[i-x]='0';
                    if(i+x<n)
                    ans[i+x]='0';
                }
            }
            boolean no=false;
            for(int i=0;i<n;i++)
            {
                if(carr[i]=='1')
                {
                    boolean poss=false;
                    if(i-x>=0&&i+x<n)
                    {
                        if(ans[i-x]=='1'||ans[i+x]=='1')
                        poss=true;
                    }
                    else if(i-x>=0)
                    {
                        if(ans[i-x]=='1')
                        poss=true;
                    }
                    else if(i+x<n)
                    {
                        if(ans[i+x]=='1')
                        poss=true;
                    }
                    if(!poss)
                    {
                        no=true;
                        break;
                    }
                }
            }
            if(no)pw.println(-1);
            else
            pw.println(new String(ans));
        }
        pw.flush();
        pw.close();
    }
}