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.InputStreamReader;
import java.util.Arrays;

public class demo_C {

    public static void main(String[] args) throws java.lang.Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(br.readLine());
        while (t-- > 0) {
            char[] s = br.readLine().toCharArray();
            int x = Integer.parseInt(br.readLine()), n = s.length;
            char[] w = new char[n];
            Arrays.fill(w, '1');
            for (int i = 0; i < n; i++) {
                if (s[i] == '0') {
                    int l = i - x;
                    int r = i + x;
                    if (l >= 0) w[l] = '0';
                    if (r < n) w[r] = '0';
                }
            }
            boolean ok = true;
            for (int i = 0; i < n; i++) {
                if (s[i] == '1') {
                    int l = i - x;
                    int r = i + x;
                    if (l >= 0 && w[l] == '1' || r < n && w[r] == '1') {
                        continue;
                    } else {
                        ok = false;
                        break;
                    }
                }
            }
            if (ok) System.out.println(w);
            else System.out.println(-1);
        }

    }

}
