D. Subsequence
brute force; divide and conquer; dp; greedy; trees
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.
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 \([9, 7, 12, 20, 18]\).