equeue

AtCoder

IDabc128_d

Time2000ms

Memory256MB

Difficulty—

Your friend gave you a dequeue $D$ as a birthday present. $D$ is a horizontal cylinder that contains a row of $N$ jewels. The _values_ of the jewels are $V_1, V_2, ..., V_N$ from left to right. There may be jewels with negative values. In the beginning, you have no jewel in your hands. You can perform at most $K$ operations on $D$, chosen from the following, at most $K$ times (possibly zero): * Operation A: Take out the leftmost jewel contained in $D$ and have it in your hand. You cannot do this operation when $D$ is empty. * Operation B: Take out the rightmost jewel contained in $D$ and have it in your hand. You cannot do this operation when $D$ is empty. * Operation C: Choose a jewel in your hands and insert it to the left end of $D$. You cannot do this operation when you have no jewel in your hand. * Operation D: Choose a jewel in your hands and insert it to the right end of $D$. You cannot do this operation when you have no jewel in your hand. Find the maximum possible sum of the values of jewels in your hands after the operations. ## Constraints * All values in input are integers. * $1 \leq N \leq 50$ * $1 \leq K \leq 100$ * $-10^7 \leq V_i \leq 10^7$ ## Input Input is given from Standard Input in the following format: $N$ $K$ $V_1$ $V_2$ $...$ $V_N$ [samples]

Samples

Input #1

6 4
-10 8 2 1 2 6

Output #1

14

After the following sequence of operations, you have two jewels of values $8$ and $6$ in your hands for a total of $14$, which is the maximum result.

*   Do operation A. You take out the jewel of value $-10$ from the left end of $D$.
*   Do operation B. You take out the jewel of value $6$ from the right end of $D$.
*   Do operation A. You take out the jewel of value $8$ from the left end of $D$.
*   Do operation D. You insert the jewel of value $-10$ to the right end of $D$.

Input #2

6 4
-6 -100 50 -2 -5 -3

Output #2

Input #3

6 3
-6 -100 50 -2 -5 -3

Output #3

0

It is optimal to do no operation.

API Response (JSON)

{
  "problem": {
    "name": "equeue",
    "description": {
      "content": "Your friend gave you a dequeue $D$ as a birthday present. $D$ is a horizontal cylinder that contains a row of $N$ jewels. The _values_ of the jewels are $V_1, V_2, ..., V_N$ from left to right. There ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc128_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Your friend gave you a dequeue $D$ as a birthday present.\n$D$ is a horizontal cylinder that contains a row of $N$ jewels.\nThe _values_ of the jewels are $V_1, V_2, ..., V_N$ from left to right. There ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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