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.util.HashMap;
import java.util.Map;
public final class Main {


    public static void main(String[] args) {

        Scanner s = new Scanner(System.in);


        int TC = s.nextInt();

        tc:for (int tc = 0; tc < TC; tc++) {

            String line[] = s.next().split("");

            int x = s.nextInt();

            int[] arr = new int[line.length];

            for (int i = 0; i < line.length; i++) {

                arr[i] = 1;
            }

            for (int i = 0; i < line.length; i++) {

                int num = Integer.parseInt(line[i]);

                if (num == 0) {

                    if (i + x < line.length) arr[i+x] = 0;

                    if (i-x >= 0) arr[i-x] = 0;
                }
            }

            for (int i = 0; i <line.length; i++) {

                int num = Integer.parseInt(line[i]);

                if (num == 1) {

                    if ((i + x >= line.length || arr[i+x] == 0) && (i-x < 0 || arr[i-x] == 0)) {

                        System.out.println(-1);

                        continue tc;
                    }

                }
            }

            for (int i = 0; i <arr.length; i++) {

                System.out.print(arr[i]);
            }

            System.out.print("\n");
        }


    }
}