Space Station Promenade

Astronaut Gustav works on a space station made of $n$ modules joined in a circle, so that module $1$ is joined to module $2$, module $2$ to module $3$, and so on, with module $n$ joined to module $1$. The distance between two neighboring modules is $1$. To create artificial gravity, the station rotates at a constant speed around the center of the circle.

The station has been in space for a long time, and it is time to clean the outside of the windows. The lot has fallen on Gustav to do this. There are $m$ windows numbered from $1$ to $m$, where window $i$ is on module $a_i$. For some reason, the windows must be cleaned in exactly this order. The only entrance and exit to the station is at module $1$.

To move between modules there is a rocket-powered window elevator that travels along the outside of the station. The elevator can only move between neighboring modules, so it cannot take any shortcuts. Gustav wants to choose a route from module $1$, around to all the windows, and back to module $1$. Unfortunately there are two problems: first, the elevator has limited fuel, so Gustav must choose a route that minimizes the distance he travels. Second, the elevator's movements affect the station's rotation, so it must travel the same distance clockwise as counterclockwise.

Find the smallest distance Gustav can travel so that he starts at module $1$, visits all the windows in the correct order, returns to module $1$, and travels the same distance counterclockwise as clockwise.

The first line contains two integers $n$ and $m$: the number of modules and the number of windows ($3 \leq n \leq 10^5$ , $1 \leq m \leq 10^5$). The second line contains $m$ integers, the indices of the modules the windows are on ($1 \leq a_i \leq n$).

One integer, the smallest distance.