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
/*
 *  Created by Andrei Arhire 18/09/2020
 *  Copyright © 2020 Andrei Arhire. All rights reserved.
 */

import java.util.*;
import java.io.*;

public class Main {

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(in, out);
        out.close();
    }

    static class Task   {
        int n, t ,sw ;
        int [] ans = new int [100005];
        int [] ans2 = new int [100005];
        String s ;
        public void solve (InputReader in, PrintWriter out)   {
            t = in.nextInt() ;
            while ( t > 0 ) {
                t -- ;
                sw = 1 ;
                s = in.next() ;
                n = in.nextInt() ;
                for ( int i = 0 ; i < s.length() ; ++ i )   {
                    ans [ i ] = 1 ;
                }
                for ( int i = 0 ; i < s.length() ; ++ i )   {
                    if ( s.charAt(i) == '0' )   {
                        if ( i + n < s.length() )   {
                            ans [ i + n ] = 0 ;
                        }
                        if ( i - n >= 0 )   {
                            ans [ i - n ] = 0 ;
                        }
                    }
                }
                for ( int i = 0 ; i < s.length() ; ++ i )   {
                    ans2 [ i ] = 0 ;
                    if ( i - n >= 0 )   {
                        if ( ans [ i - n ] == 1 )   {
                            ans2 [ i ] = 1 ;
                        }
                    }
                    if ( i + n < s.length() )   {
                        if ( ans [ i + n ] == 1 )   {
                            ans2 [ i ] = 1 ;
                        }
                    }
                    if ( ( ans2 [ i ] ==  0 && s.charAt(i) == '1' ) || ( ans2 [ i ] == 1 && s.charAt(i) == '0' ) )  {
                        sw = 0 ;
                    }
                }
                if ( sw == 0 )  {
                    out.print("-1\n") ;
                }   else    {
                    for ( int i = 0 ; i < s.length() ; ++ i )   {
                        out.print(ans[i]);
                    }
                    out.print('\n');
                }
            }
        }
    }
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

    }

}