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.*;
import java.util.*;
public class Solution {
	static String str = "";
		public static void main(String[] args)throws Exception{
			Scanner input = new Scanner();
			int test = input.nextInt();
			while(test-->0) {
				String s = input.next();
				str = "";
				int n = s.length();
				int k = input.nextInt();
				char res[] =  new char[n];
				Arrays.fill(res,'1');
				for(int i =0;i<n;i++) {
					if(s.charAt(i) == '0') {
						if(i-k>=0)res[i-k] = '0';
						if(i+k<n)res[i+k] = '0';
					}
				}
				//System.out.println(Arrays.toString(res));
				if(check(res,k).equals(s)) {for(char it:res)System.out.print(it);System.out.println();}
				else System.out.println(-1);
			
				
			}
		}
		public static String check(char c[],int k ) {
			String res = "";
			for(int i =0;i<c.length;i++) {
				if(i-k>=0 && c[i-k] == '1')res+='1';
				else if(i+k<c.length && c[i+k] == '1')res+='1';
				else res+='0';
				
			}
			return res;
		}
	}
class Scanner 
{ 
    BufferedReader br; 
    StringTokenizer st; 

    public Scanner() 
    { 
        br = new BufferedReader(new
                 InputStreamReader(System.in)); 
    } 

    String next() 
    { 
        while (st == null || !st.hasMoreElements()) 
        { 
            try
            { 
                st = new StringTokenizer(br.readLine()); 
            } 
            catch (IOException  e) 
            { 
                e.printStackTrace(); 
            } 
        } 
        return st.nextToken(); 
    } 

    int nextInt() 
    { 
        return Integer.parseInt(next()); 
    } 

    long nextLong() 
    { 
        return Long.parseLong(next()); 
    } 

    double nextDouble() 
    { 
        return Double.parseDouble(next()); 
    } 

    String nextLine() 
    { 
        String str = ""; 
        try
        { 
            str = br.readLine(); 
        } 
        catch (IOException e) 
        { 
            e.printStackTrace(); 
        } 
        return str; 
    } 
} 
