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 C1400 {

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int t = sc.nextInt();
		while (t-- > 0) {
			char[] arr = sc.next().toCharArray();
			int x = sc.nextInt();
			char[] ans = new char[arr.length];
			Arrays.fill(ans, '.');
			boolean valid = true;
			for (int i = 0; i < x; i++) {
				if (i + x < arr.length)
					ans[i + x] = arr[i];
				else {
					if (arr[i] == '1') {
						valid = false;
						break;
					}
				}
			}
			for (int i = x; valid && i < ans.length; i++) {
				if (i + x >= ans.length) {
					if (ans[i - x] == '.') {
						ans[i - x] = arr[i];
					} else if (ans[i - x] != arr[i]) {
						valid = false;
						break;
					}
				} else {
					if (arr[i] == '0') {
						if (ans[i - x] == '.')
							ans[i - x] = '0';
						if (ans[i + x] == '.')
							ans[i + x] = '0';
						if (ans[i - x] == '1' || ans[i + x] == '1') {
							valid = false;
							break;
						}
					} else {
						if (ans[i - x] == '0' && ans[i + x] == '0') {
							valid = false;
							break;
						}
						if (ans[i - x] == '1' || ans[i + x] == '1') {
							continue;
						} else {
							if (ans[i - x] == '.') {
								ans[i - x] = '1';
							} else {
								ans[i + x] = '1';
							}
						}
					}
				}
			}
			if (valid) {
				for (int i = 0; i < ans.length; i++) {
					pw.print(ans[i] == '.' ? '0' : ans[i]);
				}
				pw.println();
			} else {
				pw.println(-1);
			}
		}
		pw.close();

	}

	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public Scanner(FileReader f) {
			br = new BufferedReader(f);
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

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

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public int[] nextIntArr(int n) throws IOException {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = Integer.parseInt(next());
			}
			return arr;
		}

	}

}
