human
Write me a Python program to find the maximum value of i ⋅ j - k ⋅ (a_i | a_j) over all pairs (i, j) of integers with 1 ≤ i < j ≤ n given the following:
Can you solve the below in PYTHON3?
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.
assistant
#Here is Python program to find the maximum value of i ⋅ j - k ⋅ (a_i | a_j) over all pairs (i, j) of integers with 1 ≤ i < j ≤ n.

import sys
input = sys.stdin.readline
from collections import defaultdict

for _ in range(int(input())):
    n, k = map(int, input().split())
    A = list(map(int, input().split()))
    m = 0
    while n >= (1 << m): m += 1
    dic = defaultdict(lambda: [0, 0])

    def update(x, y):
        if y > dic[x][0]:
            dic[x][0], dic[x][1] = y, dic[x][0]
        elif y > dic[x][1]:
            dic[x][1] = y

    for i, a in enumerate(A, 1):
        update(a, i)

    for i in range(m):
        for mask in range(1 << m):
            if mask >> i & 1:
                update(mask, dic[mask ^ 1 << i][0])
                update(mask, dic[mask ^ 1 << i][1])
    ans = float("-inf")
    for mask in range(1 << m):
        if dic[mask][0] and dic[mask][1]:
            ans = max(ans, dic[mask][0] * dic[mask][1] - k * mask)
    print(ans)