CF1554B.Cobb

普及/提高-

通过率：0%

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题目描述

You are given $n$ integers $a_1, a_2, \ldots, a_n$ and an integer $k$ . Find the maximum value of $i \cdot j - k \cdot (a_i | a_j)$ over all pairs $(i, j)$ of integers with $1 \le i < j \le n$ . Here, $|$ is the bitwise OR operator.

输入格式

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 $3 \cdot 10^5$ .

输出格式

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

输入输出样例

输入#1

4
3 3
1 1 3
2 2
1 2
4 3
0 1 2 3
6 6
3 2 0 0 5 6

输出#1

说明/提示

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 $f(3, 4) = 12$ .

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