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
//package codeforces;
import java.io.PrintWriter;
import java.util.*;
public class solution { 
    public static void main(String args[]){ 
    	Scanner s=new Scanner(System.in);
		PrintWriter out=new PrintWriter(System.out);
		int t=s.nextInt();
		for(int tt=0;tt<t;tt++) {
			String a=s.next();
			int x=s.nextInt();
			char ans[]=new char[a.length()];
			Arrays.fill(ans, '1');
			boolean d=true;
			for(int i=0;i<a.length();i++) {
				if(a.charAt(i)=='0') {
					if(i+x<a.length()) {
						ans[i+x]='0';
					}if(i-x>=0){
						ans[i-x]='0';
					}
				}
			}
			for(int i=0;i<a.length();i++) {
				if(a.charAt(i)=='1') {
					if(((i+x)<a.length() && ans[i+x]=='1') || ((i-x)>=0 && ans[i-x]=='1')) {
						
					}else {
						d=false;
						break;
					}
				}
			}
			if(!d) {
				out.println(-1);
				continue;
			}
			for(int i=0;i<ans.length;i++) {
				out.print(ans[i]);
			}
			out.println();
		}
	    s.close();
	    out.close();
    } 
    
    static void sort(long [] a) {
		ArrayList<Long> l=new ArrayList<>();
		for (long i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}
    static void sort(int [] a) {
		ArrayList<Integer> l=new ArrayList<>();
		for (int i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}
    static int gcd(int a, int b)
    {
      if (b == 0)
        return a;
      return gcd(b, a % b);
    }
    static void sortcol(long a[][],int c) {
		Arrays.sort(a, (x, y) -> {
			if(x[c]!=y[c])
			 return (int)( x[c] - y[c]);
			else {
				return (int)(x[1]-y[1]);
			}
		});
	}
    public static void printb(boolean ans) {
    	if(ans) {
    		System.out.println("YES");
    	}else {
    		System.out.println("NO");
    	}
    }
}
class pair implements Comparable<pair>{
	int a , b ; 
	pair(int x , int y){
		a=x;
		b=y;
	}
	public int compareTo(pair o) {
		return a != o.a ? a - o.a : b - o.b;
	}
}
