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.
t = int(input())

for tc in range(t):

    n, k = map(int, input().split())

    arr = [int(z) for z in input().split()]

    less = []; more = []
    for i in range(n):

        if arr[i] < i+1:
            less.append(i)
        else:
            more.append([arr[i], i])

    more1 = []
    more.sort()
    for i in more:
        more1.append(i[1])

    less1 = less[::-1]
    comb = less1 + more1

    m1 = comb[0]


    res = -10**18

    for i in range(1, len(comb)):
        m2 = comb[i]
        res = max(res, ((m1+1) * (m2+1) - (k * (arr[m1] | arr[m2]))))

    print(res)

    # arr2 = sorted(arr)
    #
    # m1 = arr2[0]; m2 = arr2[1]
    #
    # for i in reversed(range(n)):
    #     if arr[i] == m1:
    #         m1d = i+1
    #         break
    #
    # for i in reversed(range(n)):
    #     if arr[i] == m2 and i+1 != m1d:
    #         m2d = i+1
    #         break
    #
    # print(m1d * m2d - k * (m1 | m2))

    # arr1 = []
    # for i in range(n):
    #     arr1.append([i, i - arr[i] + 1, arr[i]])
    #
    # arr1.sort()
    #
    # a, b, c = map(int, arr1[-1])
    # d, e, f = map(int, arr1[-2])
    #
    # print(arr1)
    #
    # print(a * d - (k * (c | f)))