101172: [AtCoder]ABC117 C - Streamline

Memory Limit:256 MB Time Limit:2 S
Judge Style:Text Compare Creator:
Submit:0 Solved:0

Description

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.


Sample Input 1

2 5
10 12 1 2 14

Sample Output 1

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 $14$.

Sample Input 2

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

Sample Output 2

19

Sample Input 3

100 1
-100000

Sample Output 3

0

Input

题意翻译

你有一个数轴和 $N$ 个棋子。 你可以先将棋子放在数轴的任意整数坐标位置,同一个位置可以放置多于一个棋子。接下来移动棋子,每次移动只能选择一个位于坐标 $x$ 的棋子,移动到 $x+1$ 或者 $x−1$ 。 你还有 $M$ 个目标地点 $x_1,x_2,x_3,\cdots,x_m$ ,你要使每个目标地点都至少被 $1$ 个棋子访问到,问至少需要多少次移动。(最初放置棋子的位置也视作访问到)

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