Sequence Growing Hard

AtCoder

IDagc024_e

Time2000ms

Memory256MB

Difficulty—

Find the number of the possible tuples of sequences $(A_0,A_1,...,A_N)$ that satisfy all of the following conditions, modulo $M$: * For every $i$ $(0\leq i\leq N)$, $A_i$ is a sequence of length $i$ consisting of integers between $1$ and $K$ (inclusive); * For every $i$ $(1\leq i\leq N)$, $A_{i-1}$ is a subsequence of $A_i$, that is, there exists $1\leq x_i\leq i$ such that the removal of the $x_i$\-th element of $A_i$ would result in a sequence equal to $A_{i-1}$; * For every $i$ $(1\leq i\leq N)$, $A_i$ is lexicographically larger than $A_{i-1}$. ## Constraints * $1 \leq N,K \leq 300$ * $2 \leq M \leq 10^9$ * $N$, $K$ and $M$ are integers. ## Input Input is given from Standard Input in the following format: $N$ $K$ $M$ [samples]

Samples

Input #1

2 2 100

Output #1

5

Five tuples below satisfy the conditions:

*   $(),(1),(1,1)$
*   $(),(1),(1,2)$
*   $(),(1),(2,1)$
*   $(),(2),(2,1)$
*   $(),(2),(2,2)$

Input #2

4 3 999999999

Output #2

Input #3

150 150 998244353

Output #3

186248260

API Response (JSON)

{
  "problem": {
    "name": "Sequence Growing Hard",
    "description": {
      "content": "Find the number of the possible tuples of sequences $(A_0,A_1,...,A_N)$ that satisfy all of the following conditions, modulo $M$: *   For every $i$ $(0\\leq i\\leq N)$, $A_i$ is a sequence of length $i",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc024_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Find the number of the possible tuples of sequences $(A_0,A_1,...,A_N)$ that satisfy all of the following conditions, modulo $M$:\n\n*   For every $i$ $(0\\leq i\\leq N)$, $A_i$ is a sequence of length $i...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments