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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class SolutionC extends Thread {
    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;
        }
    }

    private static final FastReader scanner = new FastReader();
    private static final PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) {
        new Thread(null, new SolutionC(), "Main", 1 << 26).start();
    }

    public void run() {
        int t = scanner.nextInt();
        for (int i = 0; i < t; i++) {
            solve();
        }
        out.close();
    }

    private static void solve() {
        String s = scanner.next();
        int x = scanner.nextInt();
        int n = s.length();

        char[] w = new char[n];
        Arrays.fill(w, '?');
        boolean isPossible = true;

        for (int i = 0; i < n; i++) {
            if (i - x < 0 && i + x < n) {
                if (w[i+x] != '?' && s.charAt(i) != w[i+x]) {
                    isPossible = false;
                }
                w[i+x] = s.charAt(i);
            } else if (i + x >= n && i - x >= 0) {
                if (w[i-x] != '?' && s.charAt(i) != w[i-x]) {
                    isPossible = false;
                }
                w[i - x] = s.charAt(i);
            } else if (s.charAt(i) == '0' && i - x >= 0 && i + x < n) {
                if (w[i+x] == '1' || w[i-x] == '1') {
                    isPossible = false;
                }

                w[i-x] = '0';
                w[i+x] = '0';
            } else if (s.charAt(i) == '1' && i - x < 0 && i + x >= n) {
                isPossible = false;
            }
        }

        for (int i = 0; i < n; i++) {
            if (s.charAt(i) == '1' && i - x >= 0 && i + x < n) {
                if (w[i+x] == '0' && w[i-x] == '0') {
                    isPossible = false;
                }
            }
        }

        if (!isPossible) {
            out.println(-1);
        } else {
            for (int i = 0; i < n; i++) {
                if (w[i] == '?') {
                    out.print("1");
                } else {
                    out.print(w[i]);
                }
            }
            out.println();
        }
    }

}