Subsequence

1000ms

262144K

Description:

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.

Input:

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le m \le n \le 4000$$$).

The second line contains $$$n$$$ distinct integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i < 2^{31}$$$).

Output:

Print the maximal value Alice can get.

Sample Input:

6 4
15 2 18 12 13 4

Sample Output:

Sample Input:

11 5
9 3 7 1 8 12 10 20 15 18 5

Sample Output:

Sample Input:

1 1
114514

Sample Output:

Sample Input:

2 1
666 888

Sample Output:

Note:

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

Informação

Provedor Codeforces

Código CF1580D