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.util.concurrent.ThreadLocalRandom;
import java.io.*;

public class Similar {

	public static void main(String[] args) throws NumberFormatException, IOException, InterruptedException {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int t=sc.nextInt();
		loop:while(t-->0) {
			String str=sc.next();
			char[] outcome=str.toCharArray();
			int x=sc.nextInt();
			char[] inp=new char[outcome.length];
			Arrays.fill(inp, '1');
			for (int i = 0; i < inp.length; i++) {
				if(outcome[i]=='0') {
					if(i-x>-1) {
						inp[i-x]='0';
					}
					if(i+x<inp.length) {
						inp[i+x]='0';
					}
				}
			}
			char[] trier=solvefor(inp,x);
			for (int i = 0; i < trier.length; i++) {
				if(outcome[i]!=trier[i]) {
					pw.println(-1);
					continue loop;
				}
			}
			for (int i = 0; i < trier.length; i++) {
				pw.print(inp[i]);
			}
			pw.println();
		}
		pw.close();
	}

	private static char[] solvefor(char[] inp,int x) {
		char[] res=new char[inp.length];
		for (int i = 0; i < res.length; i++) {
			if(i-x>-1) {
				if(inp[i-x]=='1') {
					res[i]='1';
					continue;
				}
			}
			if(i+x<inp.length) {
				if(inp[i+x]=='1') {
					res[i]='1';
					continue;
				}
			}
			res[i]='0';
		}
		return res;
	}

	static void shuffleArray(int[] ar) {
		// If running on Java 6 or older, use `new Random()` on RHS here
		Random rnd = ThreadLocalRandom.current();
		for (int i = ar.length - 1; i > 0; i--) {
			int index = rnd.nextInt(i + 1);
			// Simple swap
			int a = ar[index];
			ar[index] = ar[i];
			ar[i] = a;
		}
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

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

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

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

		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 < arr.length; i++)
				arr[i] = nextInt();
			return arr;
		}

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

}