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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.FileNotFoundException;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Asgar Javadov
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        CBinaryStringReconstruction solver = new CBinaryStringReconstruction();
        int testCount = Integer.parseInt(in.next());
        for (int i = 1; i <= testCount; i++)
            solver.solve(i, in, out);
        out.close();
    }

    static class CBinaryStringReconstruction {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            char[] s = in.next().toCharArray();
            int x = in.nextInt();
            int n = s.length;
            if (s.length == 2 * x + 1 && s[0] != s[n - 1]) {
                out.minusOne();
                return;
            }

            for (int i = 0; i < n; ++i) {
                if (i < x && i + x >= n && s[i] == '1') {
                    out.minusOne();
                    return;
                }
            }

            char[] w = new char[s.length];

            for (int i = 0; i < n; i++) {
                if (i - x < 0) {
                    if (i + x >= n) {
                        w[i] = '0';
                    } else {
                        w[i] = s[i + x];
                    }
                } else {
                    if (i + x >= n) {
                        w[i] = s[i - x];
                    } else {
                        w[i] = compute(s[i - x], s[i + x]);
                    }
                }
            }

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

            for (int i = 0; i < n; ++i) {
                if (i - x >= 0 && i + x < n) {
                    if (s[i] == '1' && w[i - x] == '0' && w[i + x] == '0') {
                        out.minusOne();
                        return;
                    }
                } else if (i - x >= 0) {
                    if (s[i] == '1' && w[i - x] == '0') {
                        out.minusOne();
                        return;
                    }
                } else if (i + x < n) {
                    if (s[i] == '1' && w[i + x] == '0') {
                        out.minusOne();
                        return;
                    }
                }
            }

            out.println(w);
        }

        private char compute(char l, char r) {
            int left = l - '0';
            int right = r - '0';
            return (char) ((left & right) + '0');
        }

    }

    static class InputReader extends BufferedReader {
        StringTokenizer tokenizer;

        public InputReader(InputStream inputStream) {
            super(new InputStreamReader(inputStream), 32768);
        }

        public InputReader(String filename) {
            super(new InputStreamReader(Thread.currentThread().getContextClassLoader().getResourceAsStream(filename)));
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    String line = readLine();
                    if (line == null) continue;
                    tokenizer = new StringTokenizer(line);
                } catch (IOException e) {
                    throw new RuntimeException();
                }
            }
            return tokenizer.nextToken();
        }

        public Integer nextInt() {
            return Integer.valueOf(next());
        }

    }

    static class OutputWriter extends PrintWriter {
        public OutputWriter(OutputStream outputStream) {
            super(outputStream);
        }

        public OutputWriter(Writer writer) {
            super(writer);
        }

        public OutputWriter(String filename) throws FileNotFoundException {
            super(filename);
        }

        public void minusOne() {
            println(-1);
        }

        public void close() {
            super.close();
        }

    }
}

