RLE

AtCoder

IDabc249_e

Time3000ms

Memory256MB

Difficulty—

Consider the following procedure of, given a string $X$ consisting of lowercase English alphabets, obtaining a new string: * Split the string $X$ off at the positions where two different characters are adjacent to each other. * For each string $Y$ that has been split off, replace $Y$ with a string consisting of the character which $Y$ consists of, followed by the length of $Y$. * Concatenate the replaced strings without changing the order. For example, `aaabbcccc` is divided into `aaa`,`bb`,`cccc`, which are replaced by `a3`,`b2`,`c4`, respectively, which in turn are concatenated without changing the order, resulting in `a3b2c4`.If the given string is `aaaaaaaaaa` , the new string is `a10` . Find the number, modulo $P$, of strings $S$ of lengths $N$ consisting of lowercase English alphabets, such that the length of $T$ is smaller than that of $S$, where $T$ is the string obtained by the procedure above against the string $S$. ## Constraints * $1 \le N \le 3000$ * $10^8 \le P \le 10^9$ * $N$ and $P$ are integers. * $P$ is a prime. ## Input Input is given from Standard Input in the following format: $N$ $P$ [samples]

Samples

Input #1

3 998244353

Output #1

26

Those strings of which the $1$\-st, $2$\-nd, and $3$\-rd characters are all the same satisfy the condition.
For example, `aaa` becomes `a3`, which satisfies the condition, while `abc` becomes `a1b1c1`, which does not.

Input #2

2 998244353

Output #2

0

Note that if a string is transformed into another string of the same length, such as `aa` that becomes `a2`, it does not satisfy the condition.

Input #3

5 998244353

Output #3

2626

Strings like `aaabb` and `aaaaa` satisfy the condition.

Input #4

3000 924844033

Output #4

607425699

Find the number of strings satisfying the condition modulo $P$.

API Response (JSON)

{
  "problem": {
    "name": "RLE",
    "description": {
      "content": "Consider the following procedure of, given a string $X$ consisting of lowercase English alphabets, obtaining a new string: *   Split the string $X$ off at the positions where two different characters",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc249_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Consider the following procedure of, given a string $X$ consisting of lowercase English alphabets, obtaining a new string:\n\n*   Split the string $X$ off at the positions where two different characters...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments