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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.Arrays;

public class BinaryStringReconstruction {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(
                new InputStreamReader(System.in)
        );
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
        String s = br.readLine();
        int t = Integer.parseInt(s);
        for (int i = 0; i < t; i++) {
            s = br.readLine();
            int x = Integer.parseInt(br.readLine());
            char[] bin = s.toCharArray();
            char[] res = new char[bin.length];
            Arrays.fill(res, '1');
            for (int j = 0; j < bin.length; j++) {
                if (bin[j] == '0') {
                    int l = j - x;
                    if (l >= 0) {
                        res[l] = '0';
                    }
                    int r = j + x;
                    if (r < bin.length) {
                        res[r] = '0';
                    }
                }
            }
            boolean checked = true;
            for (int j = 0; j < res.length; j++) {
                int l = j - x;
                int r = j + x;
                boolean isOne = l >= 0 && res[l] == '1';
                isOne |= r < bin.length && res[r] == '1';
                char c = isOne ? '1' : '0';
                if (bin[j] != c) {
                    checked = false;
                    break;
                }
            }
            if (checked) {
                bw.write(new String(res));
            } else {
                bw.write("-1");
            }
            bw.newLine();
        }
        bw.flush();
    }
}
