D. Subsequencetime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputAlice 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.InputThe 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}).OutputPrint the maximal value Alice can get.ExamplesInput
6 4
15 2 18 12 13 4
Output
100
Input
11 5
9 3 7 1 8 12 10 20 15 18 5
Output
176
Input
1 1
114514
Output
0
Input
2 1
666 888
Output
0
NoteIn 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].
6 4
15 2 18 12 13 4

100 
['brute force', 'divide and conquer', 'dp', 'greedy', 'trees', '*2900']