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.*;
import java.util.*;

public class Main {

    static long solve(int n, int k, int[] arr) {

        long ret = Long.MIN_VALUE;
        int s = Math.max(0, n - 2 * k - 1);
        for (int i = s; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                ret = Math.max(ret, (long) (i + 1) * (j + 1) - (long) k * (arr[i] | arr[j]));
            }
        }
        return ret;
    }

    public static void main(String[] args) throws IOException {
//        System.out.println("===== input =====");
//        BufferedReader br = new BufferedReader(new FileReader("input/input1.txt"));
//        BufferedReader br2 = new BufferedReader(new FileReader("input/input1.txt"));
//        String s;
//        while ((s = br2.readLine()) != null) {
//            System.out.println(s);
//        }
//        System.out.println("===== output =====");
         BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        StringBuilder out = new StringBuilder();
        int T = Integer.parseInt(st.nextToken());
        while (T-- > 0) {
            st = new StringTokenizer(br.readLine());
            int n = Integer.parseInt(st.nextToken());
            int k = Integer.parseInt(st.nextToken());
            int[] arr = new int[n];
            st = new StringTokenizer(br.readLine());
            for (int i = 0; i < n; i++) {
                arr[i] = Integer.parseInt(st.nextToken());
            }

            out.append(solve(n, k, arr)).append("\n");
        }
        System.out.println(out);
    }
}