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.lang.reflect.Array;
import java.util.*;
import java.lang.*;
import java.io.*;
public class Solution{

    public static void main (String[] args) throws java.lang.Exception {
        FastReader sc = new FastReader();
        int testCase = sc.nextInt();
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
        while (testCase-- > 0) {
            int n = sc.nextInt();
            int k = sc.nextInt();
            int[] intArr = new int[n];
            for(int i=0; i<n; i++){
                intArr[i]  = sc.nextInt();
            }
            long aa = Long.MIN_VALUE;
            for(int i=Math.max(0, n-2*k); i<n-1; i++){
                for(int j =i+1; j<n; j++ ){
                    aa=Math.max(aa, (long)(i+1)*(long)(j+1)-k*((long)intArr[i]|(long)intArr[j]));
                }
            }
            System.out.println(aa);
        }
    }
    // Fast Reader Class
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;
        public FastReader() { 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; }
    }
}
