Struck Out

AtCoder

IDasaporo_d

Time2000ms

Memory256MB

Difficulty—

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: $N$ $M$ $K$ $A_1$ $A_2$ … $A_N$ ## Partial Scores * In the test set worth $100$ points, $M = N$. * In the test set worth another $200$ points, $N ≦ 300$ and $K ≦ 30$. * In the test set worth another $300$ points, $K ≦ 30$. [samples]

Samples

Input #1

5 2 3
10 2 8 10 2

Output #1

56

The total score is maximized when panels $1,3$ and $4$ are hit, in this order.

Input #2

5 5 2
5 2 10 5 9

Output #2

28

This case satisfies the additional constraint $M = N$ for a partial score.

Input #3

10 3 5
3 7 2 6 9 4 8 5 1 1000000000

Output #3

5000000078

API Response (JSON)

{
  "problem": {
    "name": "Struck Out",
    "description": {
      "content": "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. Takah",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "asaporo_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "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.\nTakah...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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