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:
Find the longest possible total distance Takahashi walks during the process.
A partial score can be obtained in this problem:
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
Takahashi walks the distance of $15$ if the process goes as follows:
10 6 1 2 3 6 7 9
314159265 7 21662711 77271666 89022761 156626166 160332356 166902656 298992265