B'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 <= m <= n <= 4000 ). The second line contains n distinct integers a_1, a_2, ldots, a_n ( 1 <= 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] . '...