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.util.*;

public class Main {
    static int M = 1_000_000_007;

    private static String testCase(String s, int x) {
        int n = s.length();
        boolean[] mustBeZero = new boolean[n + 1], mustBeOne = new boolean[n + 1];
        StringBuilder ans = new StringBuilder();

        for (int i = 1; i <= n; i++) {
            if (!(i > x || i + x <= n)) mustBeZero[i] = true;
        }

        for (int i = 1; i <= n; i++) {
            char c = s.charAt(i - 1);

            if (c == '0') {
                if (i > x) mustBeZero[i - x] = true;
                if (i + x <= n) mustBeZero[i + x] = true;
            }
        }

        for (int i = 1; i <= n; i++) {
            char c = s.charAt(i - 1);

            if (c == '1') {
                if (i <= x) {
                    if (i + x <= n) mustBeOne[i + x] = true;
                    else return "";
                } else if (i + x > n) {
                    if (i > x) mustBeOne[i - x] = true;
                    else return "";
                } else if (i > x && i + x <= n) {
                    if (mustBeZero[i - x] && mustBeZero[i + x]) return "";
                    else {
                        if (mustBeZero[i + x]) mustBeOne[i - x] = true;
                        else mustBeOne[i + x] = true;
                    }
                }
            }
        }

        for (int i = 1; i <= n; i++) {
            if (mustBeZero[i] && mustBeOne[i]) {
                return "";
            } else {
                if (mustBeZero[i]) ans.append('0');
                else ans.append('1');
            }
        }

        return ans.toString();
    }

    public static void main(String[] args) {
        FastScanner in = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);
        int t = in.nextInt();  // Scanner has functions to read ints, longs, strings, chars, etc.
        //in.nextLine();
        for (int tt = 1; tt <= t; ++tt) {
            String s = in.next();
            int x = in.nextInt();

            String ans = testCase(s, x);
            out.println(ans.equals("") ? "-1" : ans);
        }

        out.close();
    }

    private static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");
        String next() {
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        char[] readCharArray(int n) {
            char[] arr = new char[n];
            try {
                br.read(arr);
                br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return arr;
        }

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

        int[] readArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

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

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