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 C {
	static FastReader f = new FastReader();
	static PrintWriter out = new PrintWriter(System.out);
	
	public static void main(String[] args) {
		int t = f.nextInt();
		while(t-- > 0) {
			solve();
		}
		
		out.close();
	}

	static void solve() {
		String s = f.next();
		int x = f.nextInt();

		boolean[] bol = new boolean[s.length()];

		for(int i=0;i<s.length();i++) {
			if(s.charAt(i) == '0') {
				if(i-x >= 0) {
					bol[i-x] = true;
				}
				if(i+x < s.length()) {
					bol[i+x] = true;
				}
			}
		}

		for(int i=0;i<s.length();i++) {
			if(s.charAt(i) == '1') {
				if((0 <= i-x && !bol[i-x]) || (s.length() > i+x && !bol[i+x])) {
					continue;
				} else {
					out.println(-1);
					return;
				}
			}
		}

		for(int i=0;i<s.length();i++) {
			out.print(bol[i] ? 0 : 1);
		}
		out.println();
	}



	static class FastReader {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st;

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

		String nextLine() {
			String s = "";
			try {
				s = br.readLine();
			} catch(IOException ioe) {
				ioe.printStackTrace();
			}

			return s;
		}

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