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.util.*;
    import static java.lang.Math.max;
    import static java.lang.Math.min;
    import static java.lang.Math.abs;
    import static java.lang.Math.ceil;
    import static java.lang.Math.max;
    import static java.lang.Math.pow;
    import static java.lang.System.out;
     
    public class Codechef {
    	static Scanner s = new Scanner(System.in);
     
    	public static void main(String[] args) {
    		int t = s.nextInt();
    		while(t-->0) {
    			int n = s.nextInt();
    			long k = s.nextLong();
    			long[] arr = new long[n];
    			for(int i = 0; i < n; i++) {
    				arr[i] = s.nextLong();
    			}
    			long ans = Integer.MIN_VALUE;
    			for(int i = n-1, c = 1; i >= 0 && c <= 300; i--,c++) {
    				for(int j = i+1; j < n; j++) {
    					long temp = ((i+1L)*(j+1L)) - (k*(arr[i]|arr[j]));
    					ans = max(temp, ans);
    				}
    			}			
    			System.out.println(ans);
    		}
    	}
     
    	public static int gcd(int a, int b)
    	{
    		if (b == 0)
    			return a;
    		return gcd(b, a % b);
    	}
     
     
    	public static void printarr(int[] arr) {
    		for(int i = 0; i < arr.length; i++) {
    			System.out.print(arr[i]+" ");
    		}
    	}
     
    	public static void printarr(int arr[][]) {
    		for(int i = 0 ; i < arr.length; i++) {
    			for(int j = 0; j < arr[0].length; j++) {
    				System.out.println(arr[i][j]+" ");
    			}
    			System.out.println();
    		}
    	}
     
    	public static void takeip(int arr[]) {
    		for(int i = 0; i < arr.length; i++) {
    			arr[i] = s.nextInt();
    		}
    	}
     
    	public static void takeip(int arr[][]) {
    		for(int i = 0 ; i < arr.length; i++) {
    			for(int j = 0; j < arr[0].length; j++) {
    				arr[i][j] = s.nextInt();
    			}
    		}
    	}
    }