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.util.Arrays;

public class C {

	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader file = new BufferedReader(new InputStreamReader(System.in));
		int inputs = Integer.parseInt(file.readLine());
		while(inputs-->0) {
			String s = file.readLine();
			int n = s.length();
			int x = Integer.parseInt(file.readLine());
			
			int[] arr = new int[n];
			Arrays.fill(arr, 1);
			
			for(int i = 0; i < n; i++) {
				if(s.charAt(i) == '0') {
					if(i+x<n) {
						arr[i+x] = 0;
					}
					if(i-x>=0) {
						arr[i-x] = 0;
					}
				}
			}
			StringBuilder ans = new StringBuilder();
			boolean pos = true;
			for(int i = 0; i < n; i++) {
				ans.append(arr[i]);
				if(s.charAt(i) == '1') {
					boolean found = false;
					if(i+x<n && arr[i+x] == 1) {
						found = true;
					}
					if(i-x>=0 && arr[i-x] == 1) {
						found = true;
					}
					if(!found) {
						pos = false;
						break;
					}
				}
			}
			if(!pos) {
				System.out.println(-1);
			}
			else {
				System.out.println(ans);
			}
		}

	}

}
