Forbidden Tournament

AtCoder

IDagc046_f

Time4000ms

Memory256MB

Difficulty—

Given are integers $N$ and $K$, and a prime number $P$. Find the number, modulo $P$, of directed graphs $G$ with $N$ vertices that satisfy below. Here, the vertices are distinguishable from each other. * $G$ is a tournament, that is, $G$ contains no duplicated edges or self-loops, and exactly one of the edges $u\to v$ and $v\to u$ exists for any two vertices $u$ and $v$. * The in-degree of every vertex in $G$ is at most $K$. * For any four distinct vertices $a$, $b$, $c$, and $d$ in $G$, it is not the case that all of the six edges $a\to b$, $b\to c$, $c\to a$, $a\to d$, $b\to d$, and $c\to d$ exist simultaneously. ## Constraints * $4 \leq N \leq 200$ * $\frac{N-1}{2} \leq K \leq N-1$ * $10^8<P<10^9$ * $N$ and $K$ are integers. * $P$ is a prime number. ## Input Input is given from Standard Input in the following format: $N$ $K$ $P$ [samples]

Samples

Input #1

4 3 998244353

Output #1

56

Among the $64$ graphs with four vertices, $8$ are isomorphic to the forbidden induced subgraphs, and the other $56$ satisfy the conditions.

Input #2

7 3 998244353

Output #2

Input #3

50 37 998244353

Output #3

495799508

API Response (JSON)

{
  "problem": {
    "name": "Forbidden Tournament",
    "description": {
      "content": "Given are integers $N$ and $K$, and a prime number $P$. Find the number, modulo $P$, of directed graphs $G$ with $N$ vertices that satisfy below. Here, the vertices are distinguishable from each other",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 4000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc046_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given are integers $N$ and $K$, and a prime number $P$. Find the number, modulo $P$, of directed graphs $G$ with $N$ vertices that satisfy below. Here, the vertices are distinguishable from each other...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments