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.
import sys
import math

if sys.subversion[0] == "PyPy":
    import io, atexit

    sys.stdout = io.BytesIO()
    atexit.register(lambda: sys.__stdout__.write(sys.stdout.getvalue()))

    sys.stdin = io.BytesIO(sys.stdin.read())
    input = lambda: sys.stdin.readline().rstrip()

t = int(raw_input())

# python codesforces210710.py < input.txt
for zz in range(t):
    #n = int(raw_input())
    str1 = raw_input()
    n, k = str1.split(' ')
    n = int(n)
    k = int(k)
    str2 = raw_input()
    lis = str2.split(' ')
    lis = map(int, lis)
    #lis = [100000] * 100000
    #n = 100000
    #k = 100

    #print(n, k)
    #print(lis)

    lvmi = max(n * (n-1.0) - k * n, 0)
    lvfori = int(max(lvmi ** 0.5 - 500, 0))
    mma = - k * n * n

    for i in range(lvfori, n):
        for j in range(i + 1, n):
            lp = k * (lis[i] | lis[j])
            canma = (i + 1) * (j + 1) - k * (lis[i] | lis[j])
            #print(i,j, canma, lp, mma)
            mma = max(canma, mma)
    print(mma)
    #print(lvmi)
    #print(lvfori)




