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;
import java.util.ArrayList;
import java.util.Collections;
import java.util.StringTokenizer;

public class B implements Runnable {

	public static void main(String[] args) throws Exception {

		new Thread(null, new B(), "SwapnilGanguly", 1 << 24).start();
	}

	public void run() {

		SwapScanner sc = new SwapScanner();
		PrintWriter pr = new PrintWriter(System.out);

		int T = sc.nextInt();

		// Brute Force

		while (T-- > 0) {

			int n = sc.nextInt(), k = sc.nextInt();
			int[] ar = new int[n + 1];

			for (int i = 1; i <= n; i++)
				ar[i] = sc.nextInt();

			int ans = Integer.MIN_VALUE;
			int p = -1, q = -1;
			int start = Math.max(1, n - 200);

			for (int i = start; i <= n; i++) {
				for (int j = i + 1; j <= n; j++) {

					int temp = (i * j) - (k * (ar[i] | ar[j]));

					if (temp > ans) {

						ans = temp;
						p = i;
						q = j;
					}

					// System.out.println(i + " " + j + " " + temp);
				}
			}

			pr.println(ans);
			// pr.println(ar[p] + " " + ar[q]);
		}

		pr.close();
	}

	public static void sort(int[] a) {

		ArrayList<Integer> l = new ArrayList<>();

		for (int i : a)
			l.add(i);

		Collections.sort(l);

		for (int i = 0; i < a.length; i++)
			a[i] = l.get(i);
	}

	public static class SwapScanner {

		BufferedReader br;
		StringTokenizer st;

		public SwapScanner() {

			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {

			while (st == null || !st.hasMoreElements()) {

				try {

					st = new StringTokenizer(br.readLine());
				}

				catch (IOException e) {

					e.printStackTrace();
				}
			}

			return st.nextToken();
		}

		int nextInt() {

			return Integer.parseInt(next());
		}

		long nextLong() {

			return Long.parseLong(next());
		}

		double nextDouble() {

			return Double.parseDouble(next());
		}

		String nextLine() {

			String str = "";

			try {

				str = br.readLine();
			}

			catch (IOException e) {

				e.printStackTrace();
			}

			return str;
		}

		int[] readArray(int n) {

			int[] ar = new int[n];

			for (int i = 0; i < n; i++)
				ar[i] = nextInt();

			return ar;
		}
	}
}