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 Binary_String_Reconstruction {

	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;
		}

	}

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		FastReader t = new FastReader();
		PrintWriter o = new PrintWriter(System.out);
		int test = t.nextInt();

		while (test-- > 0) {
			String s = t.next();
			int k = t.nextInt();
			int n = s.length();
			int[] a = new int[n];

			Arrays.fill(a, -1);

			for (int i = 0; i < n; ++i) {
				if (s.charAt(i) == '0') {
					if (i + k < n)
						a[i + k] = 0;

					if (i - k >= 0)
						a[i - k] = 0;
				}
			}

			for (int i = 0; i < n; ++i)
				if (a[i] == -1)
					a[i] = 1;

			StringBuilder sb = new StringBuilder();

			for (int i = 0; i < n; ++i) {
				int v1 = i + k < n ? a[i + k] : 0;
				int v2 = i - k >= 0 ? a[i - k] : 0;
				int v = v1 | v2;

				sb.append(v + "");
			}

			if (sb.toString().equals(s)) {
				for (int i = 0; i < n; ++i)
					o.print(a[i]);

				o.println();
			} else {
				o.println("-1");
			}
		}

		o.flush();
		o.close();
	}
}