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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.*;
import javafx.util.Pair;

public class Main
{
    public static boolean checkmatch(char a[],char b[])
    {
        
        for (int i = 0; i < a.length; i++) {
            if(a[i]!=b[i])
            {
                return false;
            }
        }
        return true;
    }
  
    public static void main(String[] args)
    {
       FastScanner input = new FastScanner();
       
       
        int tc = input.nextInt();
        while (tc-- > 0) {
           char s[] = input.next().toCharArray();
       int x = input.nextInt();
       
       char w[] = new char[s.length];
       Arrays.fill(w, '1');
        for (int i = 0; i < s.length; i++) {
            if(s[i]=='0')
            {
                if(i+x<s.length)
                {
                    w[i+x] ='0';
                }
                if(i-x>=0)
                {
                    w[i-x] = '0';
                }
            }
        }
        char test[] = new char[s.length];
        Arrays.fill(test, '0');
//        System.out.println(Arrays.toString(w));
        for (int i = 0; i <s.length; i++) {
            if(i-x>=0)
            {
                if(w[i-x]=='1')
                {
                    test[i] = '1';
                }
            }
            if(i+x<s.length)
            {
                if(w[i+x]=='1')
                {
                    test[i] = '1';
                }
            }
        }
        if(checkmatch(test, s))
        {
            System.out.println(w);
        } 
        else
        {
            System.out.println("-1");
        }
        }
        
    }
   
    static class FastScanner
    {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        String next()
        {
            while (!st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {

            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine() throws IOException
        {
            return br.readLine();
        }
    }

}
