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.Arrays;
import java.util.Scanner;

public class Main {

    private static final Scanner scanner = new Scanner(System.in);

    private void run() {
        int T = scanner.nextInt();
        while ((T--) > 0) {
            String s;
            while ((s = scanner.nextLine()).length() == 0);
            int N = s.length();
            int x = scanner.nextInt();

            boolean[] vis = new boolean[N];
            Arrays.fill(vis, true);
            for (int i = 0; i < N; ++i) {
                if (s.charAt(i) == '0') {
                    int L = i - x;
                    int R = i + x;
                    if (L >= 0 && L < N) vis[L] = false;
                    if (R >= 0 && R < N) vis[R] = false;
                }
            }
            boolean ok = true;
            for (int i = 0; i < N; ++i) {
                if (s.charAt(i) == '1') {
                    int left = i - x;
                    int right = i + x;
                    boolean has = false;
                    if (left >= 0 && left < N && vis[left]) has = true;
                    if (right >= 0 && right < N && vis[right]) has = true;
                    if (!has) {
                        ok = false;
                    }
                }
            }
            if (ok) {
                for (int i = 0; i < N; ++i) {
                    if (vis[i]) System.out.print("1");
                    else System.out.print("0");
                }
                System.out.println();
            } else {
                System.out.println("-1");
            }
        }
    }

    public static void main(String[] args) {
        new Main().run();
    }
}
