human
PYTHON3 solution for "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.":


 Give 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?
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.
 def solve(n,k,arr):
    best = (1)*(2) - k * (arr[0] | arr[1])
    if n < 500:
        for i in range(n):
            for j in range(i+1,n):
                or_aij = arr[i] | arr[j]
                new = (i+1)*(j+1) - k * or_aij
                if new > best:
                    best = new
    else:
        for i in reversed(range(n-100, n)):
            for j in range(i-100, i):
                or_aij = arr[i] | arr[j]
                new = (i+1)*(j+1) - k * or_aij
                if new > best:
                    best = new
    return best
import os
import io
# import time
# a=time.time()
if __name__ == "__main__":
    input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline

    T = int(input().decode().strip())
    for t in range(T):
        n,k = [int(x) for x in input().decode().strip().split(" ")]
        arr = [int(x) for x in input().decode().strip().split(" ")]
        res = solve(n,k,arr)
        print(res)