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You are given an array A consisting of N integers and an integer X. Your goal is to have as many equal integers as possible in the array. To achieve this goal, you can do the following operation:
Choose an index i (1 ≤ i ≤ N) and set $A_{i} = A_{i} \oplus X$, where $\oplus$ denotes the [bitwise xor operation].

Find the maximum number of equal integers you can have in the final array and the minimum number of operations to obtain these many equal integers.

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

• The first line of the input contains a single integer T denoting the number of test cases. The description of T test cases follows.
• Each test case contains two lines of input.
• The first line of each test case contains two space-separated integers N, X.
• The second line of each test case contains $N space-separated integers A_{1}, A_{2}, \dots, A_{N}$.

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

For each test case, print a single line containing two space-separated integers - first, the maximum number of equal integers in the final array and second, the minimum number of operations to achieve these many equal integers.

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

$1 ≤ T ≤ 10^{4}$
$1 ≤ N ≤ 10^{5}$
$0 ≤ X ≤ 10^{9}$
$0 ≤ A_{i} ≤ 10^{9}$
- The sum of $N$ over all test cases does not exceed $5 \cdot 10^{5}$.

------ subtasks ------

Subtask #1 (100 points): Original constraints

----- Sample Input 1 ------
3
3 2
1 2 3
5 100
1 2 3 4 5
4 1
2 2 6 6

----- Sample Output 1 ------
2 1
1 0
2 0

----- explanation 1 ------
Test case $1$: One way to obtain $2$ equal integers is to set $A_{1} = A_{1} \oplus 2$ $\; = 1 \oplus 2 = 3$. So the array becomes $[3, 2, 3]$. There is no way to obtain $3$ equal integers in the final array.

Test case $2$: There is no way to obtain more than one equal integer.

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