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.util.*;
import java.io.IOException;
import java.io.InputStreamReader;

public class probC {
	

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		FastReader scan = new FastReader();
		int tt = scan.nextInt();
		for(int iter = 0; iter < tt; iter++) {
			char[] arr = scan.next().toCharArray();
			int n = scan.nextInt();
			int len = arr.length;
			char[] ans = new char[len];
			Arrays.fill(ans, '1');
			for(int i = 0; i < len; i++) {
				if(arr[i] == '0') {
					if(legel(i - n, len)) ans[i - n] = '0';
					if(legel(i + n, len)) ans[i + n] = '0';
				}
			}
			boolean works = true;
			for(int i = 0; i < len; i++) {
				if(arr[i] == '1') {
					if(legel(i - n, len) && ans[i - n] == '1') continue;
					if(legel(i + n, len) && ans[i + n] == '1') continue;
					works = false;
				}
			}
			if(!works) System.out.println(-1);
			else System.out.println(ans);
			
		}
	}
	
	static boolean legel(int x, int n) {
		return x < n &&  x >= 0;
	}

	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			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;
		}
	}


}

//class Pair<U, V> {
//	public final U first;   	// first field of a Pair
//	public final V second;  	// second field of a Pair
//
//	// Constructs a new Pair with specified values
//	private Pair(U first, V second)
//	{
//		this.first = first;
//		this.second = second;
//	}
//
////	@Override
////	// Checks specified object is "equal to" current object or not
////	public boolean equals(Object o)
////	{
////		if (this == o)
////			return true;
////
////		if (o == null || getClass() != o.getClass())
////			return false;
////
////		Pair<?, ?> pair = (Pair<?, ?>) o;
////
////		// call equals() method of the underlying objects
////		if (!first.equals(pair.first))
////			return false;
////		return second.equals(pair.second);
////	}
//
////	@Override
////	// Computes hash code for an object to support hash tables
////	public int hashCode()
////	{
////		// use hash codes of the underlying objects
////		return 31 * first.hashCode() + second.hashCode();
////	}
//
////	@Override
////	public String toString()
////	{
////		return "(" + first + ", " + second + ")";
////	}
////
////	// Factory method for creating a Typed Pair immutable instance
//	public static <U, V> Pair <U, V> of(U a, V b)
//	{
//		// calls private constructor
//		return new Pair<>(a, b);
//	}
//}