Cobb

Description:

Input:

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10\,000$$$)  — the number of test cases.

The first line of each test case contains two integers $$$n$$$ ($$$2 \le n \le 10^5$$$) and $$$k$$$ ($$$1 \le k \le \min(n, 100)$$$).

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le n$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases doesn't exceed $$$3 \cdot 10^5$$$.

Output:

For each test case, print a single integer  — the maximum possible value of $$$i \cdot j - k \cdot (a_i | a_j)$$$.

Sample 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

Sample Output:

-1
-4
3
12

Note:

Let $$$f(i, j) = i \cdot j - k \cdot (a_i | a_j)$$$.

In the first test case,

• $$$f(1, 2) = 1 \cdot 2 - k \cdot (a_1 | a_2) = 2 - 3 \cdot (1 | 1) = -1$$$.
• $$$f(1, 3) = 1 \cdot 3 - k \cdot (a_1 | a_3) = 3 - 3 \cdot (1 | 3) = -6$$$.
• $$$f(2, 3) = 2 \cdot 3 - k \cdot (a_2 | a_3) = 6 - 3 \cdot (1 | 3) = -3$$$.

So the maximum is $$$f(1, 2) = -1$$$.

In the fourth test case, the maximum is $$$f(3, 4) = 12$$$.