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.*;
public class P1400C {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int tests = Integer.parseInt(in.nextLine());
        for (int i = 0; i < tests; i++) {
            String line = in.nextLine();
            int x = Integer.parseInt(in.nextLine());
            int[] arr = new int[line.length()];
            Arrays.fill(arr, 1);
            for (int k = 0; k < line.length(); k++) {
                if (line.charAt(k) == '0') {
                    if (k >= x) arr[k - x] = 0;
                    if (k + x < line.length()) arr[k + x] = 0;
                }
            }
            boolean exit = false;
            for (int k = 0; k < line.length(); k++) {
                if (line.charAt(k) == '1') {
                    if ((k - x < 0 || arr[k - x] == 0) && (k + x >= line.length() || arr[k + x] == 0)) {
                        System.out.println(-1);
                        exit = true;
                        break;
                    }
                }
            }
            if (!exit) {
                for (int a : arr) {
                    System.out.print(a);
                }
                System.out.println();
            }

        }
    }
}
