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.

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] $ .