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 C {
    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        int t = input.nextInt();
        input.nextLine();
        for(int i = 0; i < t; i++) {
            String line = input.nextLine();
            int x = input.nextInt();
            input.nextLine();
            int[] binary = new int[line.length()];
            Arrays.fill(binary, - 1);
            boolean works = true;
            for(int k = 0; k < line.length(); k++) {
                int cur = Integer.parseInt(line.substring(k, k + 1));
                if(cur == 0) {
                    if(k >= x) {
                        if(binary[k - x] == 1) {
                            works = false;
                            break;
                        } else {
                            binary[k - x] = 0;
                        }
                    }
                    if(k + x < line.length()) {
                        if(binary[k + x] == 1) {
                            works = false;
                            break;
                        } else {
                            binary[k + x] = 0;
                        }
                    }
                } else {
                    boolean temp = false;
                    if(k >= x) {
                        if(binary[k - x] == 0) {

                        } else {
                            binary[k - x] = 1;
                            temp = true;
                        }
                    }
                    if(k + x < line.length() && !temp) {
                        if(binary[k + x] == 0) {

                        } else {
                            binary[k + x] = 1;
                            temp = true;
                        }
                    }
                    if(!temp) {
                        works = false;
                        break;
                    }
                }
            }
            if(!works) {
                System.out.println(-1);
            } else {
                for(int k = 0; k < line.length(); k++) {
                    if(binary[k] == -1) {
                        System.out.print(0);
                        continue;
                    }
                    System.out.print(binary[k]);
                }
                System.out.println();
            }

        }
    }
}
