B. Cobb
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

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 $i \cdot j - k \cdot (a_i | a_j)$.

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

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 $f(3, 4) = 12$.