{"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.\nTakahashi 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 $i \\times A_{p_i}$.\nHe 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.\n\n## Constraints\n\n*   $1 ≦ M ≦ N ≦ 100,000$\n*   $1 ≦ K ≦ min(300,N)$\n*   $1 ≦ A_i ≦ 10^{9}$\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$ $M$ $K$\n$A_1$ $A_2$ … $A_N$\n\n## Partial Scores\n\n*   In the test set worth $100$ points, $M = N$.\n*   In the test set worth another $200$ points, $N ≦ 300$ and $K ≦ 30$.\n*   In the test set worth another $300$ points, $K ≦ 30$.\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"asaporo_d","tags":[],"sample_group":[["5 2 3\n10 2 8 10 2","56\n\nThe total score is maximized when panels $1,3$ and $4$ are hit, in this order."],["5 5 2\n5 2 10 5 9","28\n\nThis case satisfies the additional constraint $M = N$ for a partial score."],["10 3 5\n3 7 2 6 9 4 8 5 1 1000000000","5000000078"]],"created_at":"2026-03-03 11:01:14"}}