Score : 700 points
There are N panels arranged in a row in Takahashi's house, numbered 1 through N. The i-th panel has a number A_i written on it. Takahashi is playing by throwing balls at these panels.
Takahashi threw a ball K times. Let the panel hit by a boll in the i-th throw be panel p_i. He set the score for the i-th throw as i \times A_{p_i}.
He was about to calculate the total score for his throws, when he realized that he forgot the panels hit by balls, p_1,p_2,...,p_K. The only fact he remembers is that for every i (1 ≦ i ≦ K-1), 1 ≦ p_{i+1}-p_i ≦ M holds. Based on this fact, find the maximum possible total score for his throws.
The input is given from Standard Input in the following format:
N M K A_1 A_2 … A_N
Print the maximum possible total score for Takahashi's throws.
5 2 3 10 2 8 10 2
56
The total score is maximized when panels 1,3 and 4 are hit, in this order.
5 5 2 5 2 10 5 9
28
This case satisfies the additional constraint M = N for a partial score.
10 3 5 3 7 2 6 9 4 8 5 1 1000000000
5000000078