You are given n integers a_1, a_2, …, a_n and an integer k. Find the maximum value of i ⋅ j - k ⋅ (a_i | a_j) over all pairs (i, j) of integers with 1 ≤ i < j ≤ n. Here, | is the [bitwise OR operator](https://en.wikipedia.org/wiki/Bitwise_operation#OR).

Input

The first line contains a single integer t (1 ≤ t ≤ 10 000) — the number of test cases.

The first line of each test case contains two integers n (2 ≤ n ≤ 10^5) and k (1 ≤ k ≤ min(n, 100)).

The second line of each test case contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ n).

It is guaranteed that the sum of n over all test cases doesn't exceed 3 ⋅ 10^5.

Output

For each test case, print a single integer — the maximum possible value of i ⋅ j - k ⋅ (a_i | a_j).

Example

Input


4
3 3
1 1 3
2 2
1 2
4 3
0 1 2 3
6 6
3 2 0 0 5 6


Output


-1
-4
3
12

Note

Let f(i, j) = i ⋅ j - k ⋅ (a_i | a_j).

In the first test case, 

  * f(1, 2) = 1 ⋅ 2 - k ⋅ (a_1 | a_2) = 2 - 3 ⋅ (1 | 1) = -1. 
  * f(1, 3) = 1 ⋅ 3 - k ⋅ (a_1 | a_3) = 3 - 3 ⋅ (1 | 3) = -6. 
  * f(2, 3) = 2 ⋅ 3 - k ⋅ (a_2 | a_3) = 6 - 3 ⋅ (1 | 3) = -3. 



So the maximum is f(1, 2) = -1.

In the fourth test case, the maximum is f(3, 4) = 12.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Khater
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        BCobb solver = new BCobb();
        solver.solve(1, in, out);
        out.close();
    }

    static class BCobb {
        public void solve(int testNumber, Scanner sc, PrintWriter pw) {
            int t = 1;
            t = sc.nextInt();
            while (t-- > 0) {
                int n = sc.nextInt();
                int k = sc.nextInt();
                pair[] arr = new pair[n];
                long max = Long.MIN_VALUE;
                for (int i = 0; i < n; i++) {
                    arr[i] = new pair(sc.nextInt(), i + 1);
                    if (i > 0) {
                        max = Math.max(max, 1l * i * (i + 1) - 1l * k * (arr[i].x | arr[i - 1].x));
                    }
                }

                Arrays.sort(arr);
                for (int i = 0; i < n - 1; i++) {
                    for (int j = i + 1; j < i + k + 1 && j < n; j++) {
                        long tmp = 1l * arr[i].id * arr[j].id - 1l * k * (arr[i].x | arr[j].x);
                        max = Math.max(max, tmp);
                    }
                }
                pw.println(max);
            }

        }

        public class pair implements Comparable<pair> {
            int x;
            int id;

            public pair(int x, int id) {
                this.x = x;
                this.id = id;
            }

            public int compareTo(pair o) {
                return x == o.x ? id - o.id : x - o.x;
            }

        }

    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(FileReader r) {
            br = new BufferedReader(r);
        }

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

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

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

    }
}

