A14663. 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 $\\min(a\_i, a\_{i + 1}, \\ldots, a\_j)$ .</p><p>Alice wants you to help her to maximize the value of the subsequence she choose.</p><p>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.

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 $[9, 7, 12, 20, 18]$ .