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.

Sample Input 1

3 1
2 3 5

Sample Output 1

2

You can make not less than one integer $i(3 \\le i \\le N)$ satisfy $A_1 \\le A_i \\le A_2$ by performing the operation as follows.

• Choose $i=3$, and decrease $A_i$ by $1$.
• Choose $i=2$, and increase $A_i$ by $1$.

Since it is impossible to achieve the goal with less than $2$ operation, the answer is $2$.

Sample Input 2

5 2
1 4 2 3 5

Sample Output 2

0

You may already have achieved the goal from the start.

Sample Input 3

8 5
15 59 64 96 31 17 88 9

Sample Output 3

35