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
from math import *
import builtins
import string
import bisect

alphabets = list(string.ascii_lowercase)
ALPHABETS = list(string.ascii_uppercase)

# # For getting input from input.txt file
# sys.stdin = open('input.txt', 'r')
#
# # Printing the Output to output.txt file
# sys.stdout = open('output.txt', 'w')

# input = sys.stdin.readline


def print(x, end='\n'):
    sys.stdout.write(str(x) + end)


# IO helpers
def get_int():
    return int(input())


def get_list_ints():
    return list(map(int, input().split()))


def get_char_list():
    s = input()
    return list(s[:len(s)])


def get_tuple_ints():
    return tuple(map(int, input().split()))


def print_iterable(p):
    print(" ".join(map(str, p)))


def floorSearch(arr, low, high, x):
    if low > high:
        return -1
    if x >= arr[high]:
        return high
    mid = int((low + high) / 2)
    if arr[mid] == x:
        return mid
    if mid > 0 and arr[mid - 1] <= x < arr[mid]:
        return mid - 1
    if x < arr[mid]:
        return floorSearch(arr, low, mid - 1, x)
    return floorSearch(arr, mid + 1, high, x)


def binary_search(arr, x):
    low = 0
    high = len(arr) - 1
    mid = 0
    while low <= high:
        mid = (high + low) // 2
        if arr[mid] < x:
            low = mid + 1
        elif arr[mid] > x:
            high = mid - 1
        else:
            return mid
    return high


def main():
    p = get_int()
    for q in range(p):
        n, k = get_list_ints()
        ls = get_list_ints()
        final = []
        for i in range(n):
            final += [[ls[i], i+1]]
        ans = final[0][1]*final[1][1] - k*(final[0][0] | final[1][0])
        for i in range(n-1):
            if final[i][1]*final[i+1][1] - k*(final[i][0] | final[i+1][0]) > ans:
                ans = final[i][1]*final[i+1][1] - k*(final[i][0] | final[i+1][0])
        print(ans)
    pass


if __name__ == '__main__':
    main()
