You are given a sequence of distinct integers  $a_1, a_2, \ldots, a_n$ and an integer $x$ and you have to perform the following operations:

1. Remove the current minimum from $a$. This operation costs $x$.
2. Remove the current maximum from $a$. This operation costs the number of elements located on the right to the maximum. Formally, if the maximum is $a_i$ and the current size of the sequence is $k$,  then the cost will be $k$ - $i$ 

What is the minimum cost to erase the whole sequence?

Input format

• First line: Two integers $n$  and $x$  ($1\leq n \leq 10^6$ , $1\leq x \leq 10^9$) denoting the size of the sequence and the cost of the first type of operation
• Second line: A sequence $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$)
• It is guaranteed that all elements of $a$ are distinct.

Output format

Print an integer denoting the minimum cost to erase the whole sequence.