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.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;

public class tr1 {
	static PrintWriter out;
	static StringBuilder sb;
	static int n, z, k;
	static long mod = (long) 1e9 + 7;
	static int[][] memo;
	static String s;
	static int[][] ad;
	static TreeMap<Long, Integer>[] gs;
	static long inf = Long.MAX_VALUE;
	static int[] color;
	static ArrayList<Integer> o;
	static char[][] g;
	static boolean[] vis, vis1;
	static long[] f;
	static int[] a;
	static int lj;
	static int[][] mat;

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		out = new PrintWriter(System.out);
		int t = sc.nextInt();
		while (t-- > 0) {
			char[] a = sc.nextLine().toCharArray();
	         n=a.length;
			int x = sc.nextInt();
			char[] ans = new char[n];
			Arrays.fill(ans, '1');
			for (int i = 0; i < n; i++) {
				if (a[i] == '0') {
					if (i + x < n)
						ans[i+x] = '0';
					if (i - x >= 0)
						ans[i-x] = '0';
				}
			}
		//	System.out.println();
			char[] pr = new char[n];
			for (int i = 0; i < n; i++) {
				pr[i] = '0';
				if (i - x >= 0 && ans[i - x] == '1')
					pr[i] = '1';
				if (i + x < n && ans[i + x] == '1')
					pr[i] = '1';
			}
			if (new String(pr).equals(new String(a)))
				out.println(new String(ans));
			else
				out.println(-1);
		}
		out.flush();
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

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

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

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

		public String nextLine() throws IOException {
			return br.readLine();
		}

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

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

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

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

		public int[] nextArrInt(int n) throws IOException {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		public long[] nextArrLong(int n) throws IOException {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}