There are always many repetitive tasks in life. Iris always dislikes them, so she refuses to repeat them. However, time cannot be turned back; we only have to move forward.

Formally, Iris has an integer sequence $$$a_1, a_2, \ldots, a_n$$$, where each number in the sequence is between $$$1$$$ and $$$w$$$, inclusive. It is guaranteed that $$$w \geq 2$$$.

Iris defines an operation as selecting two numbers $$$a_i, a_{i+1}$$$ satisfying $$$a_i = a_{i+1}$$$, and then changing them to two arbitrary integers within the range $$$[1, w]$$$. Iris does not like equality, so she must guarantee that $$$a_i \neq a_{i+1}$$$ after the operation. Two identical pairs $$$a_i, a_{i+1}$$$ can be selected multiple times.

Iris wants to know the maximum possible sum of all elements of $$$a$$$ after several (possible, zero) operations, as well as the minimum number of operations required to achieve this maximum value.

Input format:
Each test contains multiple test cases. The first line contains an integer $$$t$$$ ($$$1 \leq t \leq 10^5$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains two integers $$$n$$$ and $$$w$$$ ($$$1 \leq n \leq 2\cdot 10^5$$$, $$$2 \leq w \leq 10^8$$$) — the length of the array, and the maximum allowed value of the elements.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \leq a_i \leq w$$$) — the elements in the array.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^6$$$.
Output format:
For each test case, output two integers — the maximum possible sum of all elements of $$$a$$$ and the minimum number of operations required, respectively.
Example Input 0:
2
5 8
1 2 3 4 5
7 5
3 1 2 3 4 1 1

Example Output 0:
15 0
34 6

Notes:
In the first test case, no operation can be performed so the answers are $$$\sum a_i = 15$$$ and $$$0$$$, respectively.

In the second test case, the operations can be performed as follows:

$$$$$$[3, 1, 2, 3, 4, \underline{1, 1}] \rightarrow [3, 1, 2, 3, \underline{4, 4}, 5] \rightarrow [3, 1, 2, \underline{3, 3}, 5, 5] \rightarrow [3, 1, \underline{2, 2}, 5, 5, 5] \rightarrow [3, \underline{1, 1}, 5, 5, 5, 5] \rightarrow [\underline{3, 3}, 5, 5, 5, 5, 5] \rightarrow [4, 5, 5, 5, 5, 5, 5]$$$$$$

It can be shown this is optimal, so we should output $$$\sum a_i = 34$$$ and the number of operations, $$$6$$$, respectively.

Example input:
2
5 8
1 2 3 4 5
7 5
3 1 2 3 4 1 1


Example output:
15 0
34 6