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.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;

public class Cobb {
    public static void main(String[] args) throws IOException {
        // BufferedReader br = new BufferedReader(new FileReader("input.txt"));
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        handleMultipleTestCase(br);
    }

    private static void handleMultipleTestCase(BufferedReader br) throws IOException {
        int T = Integer.parseInt(br.readLine());
        for (int i = 0; i < T; i++) {
            int[] NK = Arrays.stream(br.readLine().split(" ")).mapToInt(Integer::parseInt).toArray();
            int N = NK[0];
            int K = NK[1];
            int[] A = Arrays.stream(br.readLine().split(" ")).mapToInt(Integer::parseInt).toArray();
            System.out.println(getResult(N, K, A));
        }
    }

    private static int getResult(int n, int k, int[] a) {
        int ans = Integer.MIN_VALUE;
        for (int i = Math.max(0, n - 201); i < n - 1; i++) {
            for (int j = i + 1; j < n; j++) {
                int I = i + 1;
                int J = j + 1;
                ans = Math.max(ans, I * J - k * (a[i] | a[j]));
            }
        }
        return ans;
    }
}