Variables

Problem Description

You are given $n$ integer constants $c_1, c_2, \dots, c_n$ and an integer $k$. You must assign integer values to $2k$ variables $x_1, x_2, \dots, x_k, y_1, y_2, \dots, y_k$ such that:

1. For all $1 \le i \le k$, we have $x_i \le y_i$.
2. For all $1 \le i \le n$, there exists at least one $j$ ($1 \le j \le k$) such that $x_j \le c_i \le y_j$.

Find the minimum possible value of $S = (y_1 + y_2 + \dots + y_k) - (x_1 + x_2 + \dots + x_k)$.

Input Format

The first line contains two integers $n$ and $k$.

The next line contains $n$ integers $c_1, c_2, \dots, c_n$.

Output Format

One integer: the minimum value of $S$.

Sample Input

5 2
-5 0 10 4 0

Sample Output

9

Constraints

There are 10 test points in total.

Test points 1, 2: $n \le 5$, $-5 \le c_i \le 5$.

Test points 3, 4, 5: $n \le 100$.

For all data, $1 \le n, k \le 10^5$ and $-10^9 \le c_i \le 10^9$.

Hint

See the attached files.