C - Streamline

Score : $300$ points

Problem Statement

We will play a one-player game using a number line and $N$ pieces.

First, we place each of these pieces at some integer coordinate.

Here, multiple pieces can be placed at the same coordinate.

Our objective is to visit all of the $M$ coordinates $X_1, X_2, ..., X_M$ with these pieces, by repeating the following move:

Move: Choose a piece and let $x$ be its coordinate. Put that piece at coordinate $x+1$ or $x-1$.

Note that the coordinates where we initially place the pieces are already regarded as visited.

Find the minimum number of moves required to achieve the objective.

Constraints

• All values in input are integers.
• $1 \leq N \leq 10^5$
• $1 \leq M \leq 10^5$
• $-10^5 \leq X_i \leq 10^5$
• $X_1, X_2, ..., X_M$ are all different.

Input

Input is given from Standard Input in the following format:

$N$ $M$

$X_1$ $X_2$ $...$ $X_M$

Output

Find the minimum number of moves required to achieve the objective.

2 5
10 12 1 2 14

5

The objective can be achieved in five moves as follows, and this is the minimum number of moves required.

• Initially, put the two pieces at coordinates $1$ and $10$.
• Move the piece at coordinate $1$ to $2$.
• Move the piece at coordinate $10$ to $11$.
• Move the piece at coordinate $11$ to $12$.
• Move the piece at coordinate $12$ to $13$.
• Move the piece at coordinate $13$ to $14$.

3 7
-10 -3 0 9 -100 2 17

19

100 1
-100000

0