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 File {
    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner() {
            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());
        }
    }		
	
    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
		
		
		
		int T = sc.nextInt();
		
		for (int t = 1; t <= T; t++) {
			String s = sc.next();
			int x = sc.nextInt();
			int N = s.length();
			
			char[] w = new char[N];
			Arrays.fill(w, '1');
			
			// Place the 0's that must be placed.
			for (int i = 0; i < N; i++) {
				if (s.charAt(i) == '0') {					
					if (i - x >= 0) {
						w[i-x] = '0';
					}
					if (i + x < N) {
						w[i+x] = '0';
					}
				}
			}
			
			boolean isValid = true;
			
			// After that the remaining positions are '1'.
			for (int i = 0; i < N; i++) {
				if (s.charAt(i) == '1') {
					int ones = 0;
					if (i-x >= 0 && w[i-x] == '1') {
						ones++;
					}
					if (i+x < N && w[i+x] == '1') {
						ones++;
					}
					
					if (ones == 0) {
						isValid = false;
						break;
					}
				}
			}
			
			if (isValid) {
				out.println(new String(w));
			}
			else {
				out.println(-1);
			}
		}
		
		
		
		out.close();
	}
}












	