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.PrintWriter;
import java.util.*;

public class T3 extends PrintWriter {
    public T3() {
        super(System.out);
    }

    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        T3 main = new T3();
        int n = s.nextInt();
        s.nextLine();
        while (n-- > 0) {
            main.mainPrint(s);
        }
        main.flush();
    }

    private void mainPrint(Scanner s) {
        String b = s.nextLine();
        int n = s.nextInt();
        s.nextLine();
        char[] w = new char[b.length()];
        Arrays.fill(w,'1');
        for (int i = 0; i < b.length(); i++){
            if (b.charAt(i)=='0'){
                if (i>=n) w[i-n] = '0';
                if (i+n<b.length()) w[i+n] = '0';
            }
        }
        for (int i = 0;i< b.length(); i++) {
            if (b.charAt(i)=='1'){
                if (!(i>=n && w[i-n] == '1') && !(i+n<b.length() && w[i+n]=='1')) {
                    println(-1);
                    return;
                }
            }
        }
        println(new String(w));
    }
}