Problem Statement

You are given an integer sequence of length $N$: $A=(A_1,A_2,\dots,A_N)$. You can perform the following operation any number of times (possibly zero).

• Choose an integer $i$ such that $1 \le i \le N$, and increase or decrease $A_i$ by $1$.

Your goal is to make at least $M$ integers $i(3 \le i \le N)$ satisfy $A_1 \le A_i \le A_2$. Find the minimum number of operations required to achieve this goal.

Constraints

• $3 \le N \le 2 \times 10^5$
• $1 \le M \le N-2$
• $1 \le A_i \le 10^9$

Input

The input is given from Standard Input in the following format:

N M
A_1 A_2 \dots A_N

Output

Print the minimum number of operations required.