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.Comparator;
import java.util.List;

public class BinaryStringReconstruction { // Template for CF
    public static class ListComparator implements Comparator<List<Integer>> {

        @Override
        public int compare(List<Integer> l1, List<Integer> l2) {
            for (int i = 0; i < l1.size(); ++i) {
                if (l1.get(i).compareTo(l2.get(i)) != 0) {
                    return l1.get(i).compareTo(l2.get(i));
                }
            }
            return 0;
        }
    }

    public static class Pair {
        int first;
        int second;

        public Pair(int first, int second) {
            this.first = first;
            this.second = second;
        }

        public int getFirst() {
            return first;
        }

        public int getSecond() {
            return second;
        }

        @Override
        public String toString() {
            return first + " " + second;
        }
    }

    public static void main(String[] args) throws IOException {
        // Check for int overflow!!!!
        // Should you use a long to store the sum or smthn?
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);

        int T = Integer.parseInt(f.readLine());
        for (int i = 0; i < T; i++) {
            String str = f.readLine();
            int n = Integer.parseInt(f.readLine());
            StringBuilder sb = new StringBuilder(str.length());
            for (int j = 0; j < str.length(); j++) {
                sb.append('1');
            }
            for (int j = 0; j < str.length(); j++) {
                if (str.charAt(j) - '0' == 0) {
                    if (j - n >= 0) {
                        sb.setCharAt(j - n, '0');
                    }
                    if (j + n < str.length()) {
                        sb.setCharAt(j + n, '0');
                    }
                }
            }
            boolean works = true;
            for (int j = 0; j < str.length(); j++) {
                boolean check = false;
                if (str.charAt(j) - '0' == 1) {
                    if (j - n >= 0) {
                        if (sb.charAt(j - n) - '0' == 1) {
                            check = true;
                        }
                    }
                    if (j + n < str.length()) {
                        if (sb.charAt(j + n) - '0' == 1) {
                            check = true;
                        }
                    }
                    if (!check) {
                        works = false;
                    }
                }
            }
            if (!works) {
                out.println(-1);
            } else {
                out.println(sb.toString());
            }
            // System.out.println(sb.toString());

        }
        out.close();
    }

}