Subsequence
Description
Alice has an integer sequence $a$ of length $n$ and all elements are different. She will choose a subsequence of $a$ of length $m$, and defines the value of a subsequence $a_{b_1},a_{b_2},\ldots,a_{b_m}$ as $$\sum_{i = 1}^m (m \cdot a_{b_i}) - \sum_{i = 1}^m \sum_{j = 1}^m f(\min(b_i, b_j), \max(b_i, b_j)),$$ where $f(i, j)$ denotes $\min(a_i, a_{i + 1}, \ldots, a_j)$.
Alice wants you to help her to maximize the value of the subsequence she choose.
A sequence $s$ is a subsequence of a sequence $t$ if $s$ can be obtained from $t$ by deletion of several (possibly, zero or all) elements.
The first line contains two integers $n$ and $m$ ($1 \le m \le n \le 4000$).
The second line contains $n$ distinct integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i < 2^{31}$).
Print the maximal value Alice can get.
Input
The first line contains two integers $n$ and $m$ ($1 \le m \le n \le 4000$).
The second line contains $n$ distinct integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i < 2^{31}$).
Output
Print the maximal value Alice can get.
Samples
6 4
15 2 18 12 13 4
100
11 5
9 3 7 1 8 12 10 20 15 18 5
176
1 1
114514
0
2 1
666 888
0
Note
In the first example, Alice can choose the subsequence $[15, 2, 18, 13]$, which has the value $4 \cdot (15 + 2 + 18 + 13) - (15 + 2 + 2 + 2) - (2 + 2 + 2 + 2) - (2 + 2 + 18 + 12) - (2 + 2 + 12 + 13) = 100$. On top of that, the subsequence $[15, 2, 18, 12]$ is also a possible answer.
In the second example, there are a variety of subsequences with value $176$, and one of them is $[9, 7, 12, 20, 18]$.