JJ has an array A of length N and an integer X. JJ can perform the following operation at most once:
Select a [subsequence] of A and add X to all the elements of that subsequence.

For example, if A = [2, 1, 6, 3, 5] and X = 7, we can select the subsequence [2, 3, 5] and add X to all the elements. Now the array A becomes [2 + 7, 1, 6, 3 + 7, 5 + 7] = [9, 1, 6, 10, 12].

JJ wants to maximize the value of $\displaystyle \sum_{i = 2}^{N} (A_{i - 1} \oplus A_{i}).$ Can you help him to do so?

Here, $\oplus$ denotes the [bitwise XOR operation].

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------ Input Format ------

• The first line contains a single integer T — the number of test cases. Then the test cases follow.
• The first line of each test case contains two space-separated integers N and X — the size of the array A and the parameter X mentioned in the statement.
• The second line of each test case contains $N space-separated integers A_{1}, A_{2}, \ldots, A_{N}$ denoting the array A.

------ Output Format ------

For each test case, output the maximum value of $\displaystyle \sum_{i = 2}^{n} (A_{i - 1} \oplus A_{i})$ which can be obtained after applying the given operation at most once.

------ Constraints ------

$1 ≤ T ≤ 10^{5}$
$1 ≤ N ≤ 10^{5}$
$1 ≤X ≤10^{9}$
$1 ≤A_{i} ≤10^{9}$
- The sum of $N$ over all test cases does not exceed $2 \cdot 10^{5}$.

----- Sample Input 1 ------
3
2 1
1 2
4 1
2 2 3 3
5 2
5 3 6 2 8

----- Sample Output 1 ------
3
15
43

----- explanation 1 ------
Test case $1$: It is optimal to not perform the given operation. So the answer will equal $1 \oplus 2 = 3$.

Test case $2$: It is optimal to add $X = 1$ to the $2^{nd}$ and the $3^{rd}$ element. So $A$ will become $[2, 3, 4, 3]$ and the answer will be $(2 \oplus 3) + (3 \oplus 4) + (4 \oplus 3) = 15$.

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