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 javax.management.monitor.StringMonitorMBean;
import java.util.*;
import java.io.*;

public class C_BinaryStringReconstruction {
    private static final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    private static final PrintWriter pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
    private static StringTokenizer st;

    private static int readInt() throws IOException {
        while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
        return Integer.parseInt(st.nextToken());
    }

    private static int[] readIntArray(final int n) throws IOException {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = readInt();
        return a;
    }


    public static void main(String[] args) throws IOException {
        int T = readInt();
        while (T-- > 0) {
            pw.println(solve());
        }
        pw.close();
    }

    private static String solve() throws IOException {
        final byte char0 = '0';
        final byte char1 = '1';

        byte[] cs = br.readLine().getBytes();
        int x = readInt();

        int n = cs.length;

        byte[] res = new byte[n];
        Arrays.fill(res, char1);
        for (int j = 0; j < n; j++) {
            if (cs[j] == char0) {
                if (j >= x) res[j - x] = char0;
                if (j + x < n) res[j + x] = char0;
            }
        }

        for (int j = 0; j < n; j++) {
            if (cs[j] == char1
                    && (j < x || res[j - x] == char0)
                    && (j + x >= n || res[j + x] == char0))
                return "-1";
        }

        return new String(res);
    }
}

/*
1
01
1
 */
