Contest: Task: Related: TaskA TaskC

Score : $800$ points

Takahashi Lake has a perimeter of $L$. On the circumference of the lake, there is a residence of the lake's owner, Takahashi. Each point on the circumference of the lake has a coordinate between $0$ and $L$ (including $0$ but not $L$), which is the distance from the Takahashi's residence, measured counter-clockwise.

There are $N$ trees around the lake; the coordinate of the $i$-th tree is $X_i$. There is no tree at coordinate $0$, the location of Takahashi's residence.

Starting at his residence, Takahashi will repeat the following action:

- If all trees are burnt, terminate the process.
- Specify a direction: clockwise or counter-clockwise.
- Walk around the lake in the specified direction, until the coordinate of a tree that is not yet burnt is reached for the first time.
- When the coordinate with the tree is reached, burn that tree, stay at the position and go back to the first step.

Find the longest possible total distance Takahashi walks during the process.

A partial score can be obtained in this problem:

- $300$ points will be awarded for passing the input satisfying $N \leq 2000$.

- $2 \leq L \leq 10^9$
- $1 \leq N \leq 2\times 10^5$
- $1 \leq X_1 < ... < X_N \leq L-1$
- All values in input are integers.

Input is given from Standard Input in the following format:

$L$ $N$ $X_1$ $:$ $X_N$

Print the longest possible total distance Takahashi walks during the process.

10 3 2 7 9

15

Takahashi walks the distance of $15$ if the process goes as follows:

- Walk a distance of $2$ counter-clockwise, burn the tree at the coordinate $2$ and stay there.
- Walk a distance of $5$ counter-clockwise, burn the tree at the coordinate $7$ and stay there.
- Walk a distance of $8$ clockwise, burn the tree at the coordinate $9$ and stay there.

10 6 1 2 3 6 7 9

27

314159265 7 21662711 77271666 89022761 156626166 160332356 166902656 298992265

1204124749