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.Scanner;

public class p1400c {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        for (int i = 0; i < t; i++) {
            String s = sc.next();
            int x = sc.nextInt();
            StringBuilder temp = new StringBuilder();
            for (int j = 0; j < s.length(); j++){
                temp.append('1');
            }
            for (int j = 0; j < s.length(); j++) {
                if(s.charAt(j) == '0')
                {
                    int pos1 = j + x;
                    int pos2 = j - x;
                    if(pos1 < s.length())
                        temp.replace(pos1 , pos1 + 1 , "0");
                    if(pos2 >= 0)
                        temp.replace(pos2 , pos2 + 1 , "0");
                }
            }

            for (int j = 0; j < s.length(); j++) {
                if(s.charAt(j) == '1')
                {
                    char char1 = (j + x) < s.length() ? temp.charAt(j + x) : '0';
                    char char2 = (j - x) >= 0 ? temp.charAt( j - x) : '0';
                    if(char1 != '1' && char2 != '1')
                    {
                        temp = new StringBuilder("-1");
                        break;
                    }
                }
            }
            System.out.println(temp);
        }
    }
}
