| # p03899 CODE FESTIVAL 2016 Tournament Round 3 (Parallel) - Struck Out | |
| ## Problem Description | |
| 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. | |
| Constraints | |
| * 1 ≦ M ≦ N ≦ 100,000 | |
| * 1 ≦ K ≦ min(300,N) | |
| * 1 ≦ A_i ≦ 10^{9} | |
| Input | |
| The input is given from Standard Input in the following format: | |
| N M K | |
| A_1 A_2 … A_N | |
| Output | |
| Print the maximum possible total score for Takahashi's throws. | |
| Examples | |
| Input | |
| 5 2 3 | |
| 10 2 8 10 2 | |
| Output | |
| 56 | |
| Input | |
| 5 5 2 | |
| 5 2 10 5 9 | |
| Output | |
| 28 | |
| Input | |
| 10 3 5 | |
| 3 7 2 6 9 4 8 5 1 1000000000 | |
| Output | |
| 5000000078 | |
| ## Contest Information | |
| - **Contest ID**: 0 | |
| - **Problem Index**: | |
| - **Points**: 0.0 | |
| - **Rating**: 0 | |
| - **Tags**: | |
| - **Time Limit**: {'seconds': 2, 'nanos': 0} seconds | |
| - **Memory Limit**: 536870912 bytes | |
| ## Task | |
| Solve this competitive programming problem. Provide a complete solution that handles all the given constraints and edge cases. |