CF1580D.Subsequence

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.

Alice 有一个长度为 $n$ 的整数序列 $a$，且其中所有元素互不相同。她将从 $a$ 中选择一个长度为 $m$ 的子序列，并将子序列 $a_{b_1},a_{b_2},\ldots,a_{b_m}$ 的值定义为

$$\sum_{i = 1}^m (m \cdot a_{b_i}) - \sum_{i = 1}^m \sum_{j = 1}^m f(\min(b_i, b_j), \max(b_i, b_j)),$$

其中 $f(i, j)$ 表示 $\min(a_i, a_{i + 1}, \ldots, a_j)$。

Alice 希望你帮她选出一个子序列，使其值最大化。

序列 $s$ 是序列 $t$ 的子序列，当且仅当 $s$ 可通过从 $t$ 中删除若干（可能为零个或全部）元素得到。

The first line contains two integers $n$ and $m$ ($1 \le m \le n \le 4000$).

The second line contains $n$ distinct integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \lt 2^{31}$).

第一行包含两个整数 $n$ 和 $m$（$1 \le m \le n \le 4000$）。

第二行包含 $n$ 个互不相同的整数 $a_1, a_2, \ldots, a_n$（$1 \le a_i \lt 2^{31}$）。

Print the maximal value Alice can get.

输出 Alice 能获得的最大值。

In the first example, Alice can choose the subsequence $[15, 2, 18, 13]$, which has the value $4 \cdot (15 + 2 + 18 + 13) - (15 + 2 + 2 + 2) - (2 + 2 + 2 + 2) - (2 + 2 + 18 + 12) - (2 + 2 + 12 + 13) = 100$. In the second example, there are a variety of subsequences with value $176$, and one of them is $[9, 7, 12, 20, 18]$.

在第一个例子中，Alice 可以选择子序列 $[15, 2, 18, 13]$，其值为 $4 \cdot (15 + 2 + 18 + 13) - (15 + 2 + 2 + 2) - (2 + 2 + 2 + 2) - (2 + 2 + 18 + 12) - (2 + 2 + 12 + 13) = 100$。在第二个例子中，存在多种值为 $176$ 的子序列，其中之一是 $[9, 7, 12, 20, 18]$。