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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;

public class B_Rnd735 
{
	public static void main(String[] args) throws NumberFormatException, IOException
	{
		BufferedReader scan = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter out = new PrintWriter(System.out);

		String[] in;
		int tt = Integer.parseInt(scan.readLine());
		
		for(int t = 0; t < tt; t++)
		{
			in = scan.readLine().split(" ");
			int n = parse(in[0]), k = parse(in[1]);
			
			in = scan.readLine().split(" ");
			long[] ray = new long[n];
			
			for(int i = 0; i < n; i++)
				ray[i] = parse(in[i]);
			
			long ans = solve(n, k, ray);
			out.println(ans);
		}

		out.flush();
	}

	private static long solve(int n, int k, long[] ray) 
	{
		long max = Long.MIN_VALUE;
		for(int i = n - 1; i >= 0; i--)
		{
			if(((long)i + 1) * (i) < max) break;
			
			for(int j = i - 1; j >= 0; j--)
			{
				max = Math.max(max, ((long) i + 1) * (j + 1) - (k * (ray[i] | ray[j])));
				if(ray[i] == (ray[i] | ray[j]) || (long) (i + 1) * (long) (j + 1) < max) break;
			}
		}
		
		return max;
	}

	public static int parse(String num)
	{
		return Integer.parseInt(num);
	}
}