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.*;
 
public class Solution{
	static PrintWriter out=new PrintWriter(System.out);
	public static void main (String[] args) throws IOException{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		
		String[] input=br.readLine().trim().split(" ");
		
		int numTestCases=Integer.parseInt(input[0]);
		while(numTestCases-->0){
		    input=br.readLine().trim().split(" ");
		    String str=input[0];
		    int x=Integer.parseInt(br.readLine());
		    out.println(getString(str,x));
		}
		
		out.flush();
		out.close();
	}
	public static String getString(String str,int x)
	{
	    StringBuilder ans=new StringBuilder("");
	    int n=str.length();
	    for(int i=0;i<n;i++){
	        ans.append(".");
	    }
	    for(int i=0;i<n;i++){
	        if(str.charAt(i)=='0'){
	            if(i+x<n){
	                ans.setCharAt(i+x,'0');
	            }
	            if(i-x>=0 && ans.charAt(i-x)=='1'){
    	            return "-1";
    	        }
    	        if(i-x>=0){
    	            ans.setCharAt(i-x,'0');
    	        }
	        }
	        else{
	            if(i-x>=0 && ans.charAt(i-x)=='0'){
    	            if(i+x<n){
    	                ans.setCharAt(i+x,'1');
    	                continue;
    	            }
    	            else{
    	                return "-1";
    	            }
    	        }
    	        if(i-x>=0){
    	            ans.setCharAt(i-x,'1');
    	        }
    	        else if(i+x<n)
    	        {
    	            ans.setCharAt(i+x,'1');
    	        }
    	        else{
    	            return "-1";
    	        }
	        }
	    }
	    for(int i=0;i<n;i++){
	        if(ans.charAt(i)=='.'){
	            ans.setCharAt(i,'0');
	        }
	    }
	    return ans.toString();
	}
}