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.*;
import java.io.*;

//great question... had to check for 0 instead of 1.

public class Question3 {
static Scanner sc = new Scanner(System.in);
static BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
	public static void main(String[] args) throws IOException{
		int t = sc.nextInt();
		while(t-->0) {
			solve();
		}
		bw.flush();
		bw.close();
	}
	
	public static void solve() throws IOException{
		char[] arr = sc.next().toCharArray();
		int x = sc.nextInt();
		
		int n = arr.length;
		char[] brr = new char[n];
		Arrays.fill(brr, '1');
		for(int i = 0;i < n;i++) {
			
			if(arr[i] == '0') {
				if(i + x < n && i + x >= 0)brr[i + x] = '0';
				if(i - x >= 0 && i - x < n)brr[i - x] = '0';
				
			}
				
			
		}
		
		if(isValid(arr, brr, x)) {
			print(brr);
		}
		else bw.write("-1" + "\n");
		return;
		
	}
	
	public static void print(char[] a) throws IOException{
		for(char c : a)bw.write(c);
		bw.write("\n");
	}
	
	public static boolean isValid(char[] arr, char[] original, int x) {
		char[] crr = new char[original.length];
		int n = original.length;
		//from original to crr
		for(int i = 0;i < n;i++) {
			
			if(i - x >= 0 && i - x < n && original[i - x] == '1') {
				crr[i] = '1';
			}
			else if(i + x < n && i + x >= 0 && original[i + x] == '1') {
				crr[i] = original[i + x];
			}
			else crr[i] = '0';
			
			if(crr[i] != arr[i])return false;
			
		}
		
		return true;
	}
}
