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 _1400C {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        while (t-- > 0) {
            char[] ch = sc.next().toCharArray();
            int n = ch.length;
            char[] w = new char[n];
            int x = sc.nextInt();
            int flag = 0;
            Arrays.fill(w, 'f');
            for (int i = 0; i < n; i++) {
                if (ch[i] == '0') {
                    if (i - x >= 0)
                        w[i - x] = '0';
                    if (i + x < n)
                        w[i + x] = '0';
                }
            }
            for (int i = 0; i < n; i++) {
                if (ch[i] == '1') {
                    if (i + x < n && w[i + x] != '0')
                        w[i + x] = '1';
                    else if (i - x >= 0 && w[i - x] != '0')
                        w[i - x] = '1';
                    else
                        flag = 1;
                }
            }
            if (flag == 1)
                System.out.println("-1");
            else {
                for (int i = 0; i < n; i++) {
                    if (w[i] == 'f')
                        System.out.print(1);
                    else
                        System.out.print(w[i]);
                }
                System.out.println();
            }
        }
    }
}