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;
import java.util.Random;
import java.util.StringTokenizer;

public class C {
	public static void main(String[] args)
	{
		FastScanner in=new FastScanner();
		int T=in.nextInt();
		while(T-->0)
		{
			char[] arr=in.next().toCharArray();
	        int x=in.nextInt();
	        int n=arr.length;
	        char[] ans=new char[n];
	        Arrays.fill(ans, '1');
	        for(int i=0;i<n;i++)
	        {
	            if(arr[i]=='0')
	            {
	            	if(indexCheck(i+x,n)) ans[i+x]='0';
	            	if(indexCheck(i-x,n)) ans[i-x]='0';
	            }
	        }
	        boolean flag=true;
			for(int i=0;i<n;i++)
			{
				if(arr[i]=='1')
				{
					if(indexCheck(i+x,n) && ans[i+x]=='1' ) continue;
					if(indexCheck(i-x,n) && ans[i-x]=='1' ) continue;
					flag=false;
				}
			}
			if(!flag)
				System.out.println("-1");
			else
			{
				for(char c: ans)
					System.out.print(c);
				System.out.println();
			}
		}
	}
	public static boolean indexCheck(int x,int n)
	{
		return x>=0 && x<n;
	}
static final Random random=new Random();
	
	static void ruffleSort(int[] a) {
		int n=a.length;//shuffle, then sort 
		for (int i=0; i<n; i++) {
			int oi=random.nextInt(n), temp=a[oi];
			a[oi]=a[i]; a[i]=temp;
		}
		Arrays.sort(a);
	}
	
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}
}
