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.IOException;
import java.io.InputStreamReader;
import java.lang.*;
import java.util.*;

public class Main {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st;
        StringBuilder sb = new StringBuilder("");
        int t = Integer.parseInt(br.readLine());
        while(t-- != 0) {
            String s = br.readLine();
            int x = Integer.parseInt(br.readLine());
            System.out.println(Code(s , x));
        }
    }

    static String Code(String s , int x) {
        int n = s.length();
        char[] res = new char[n];
        Arrays.fill(res , '1');
        for(int i = 0 ; i < n ; i++) {
            if(s.charAt(i) == '0') {
                if(i - x >= 0) {
                    res[i-x] = '0';
                }
                if(i + x < n) {
                    res[i+x] = '0';
                }
            }
        }
        for(int i = 0 ; i < n ; i++) {
            if(s.charAt(i) == '1') {
                boolean what = false;
                if(i - x >= 0) {
                    if(res[i-x] == '1') {
                        what = true;
                    }
                }
                if(i + x < n) {
                    if(res[i+x] == '1') {
                        what = true;
                    }
                }
                if(!what) {
                    //System.out.println("i -> " + (i+1));
                    return "-1";
                }
            }
        }
        String out = new String(res);
        //System.out.println(out);
        return new String(res);
    }

}
// dp[i] = Math.max(0 , curPts + dp[i-2])
/*
7 8 4 5 7 6 8 9 7 3
[0, 0, 1, 4, 2, 2, 1, 0, 2, 2, 0]
 */