{"problem":{"name":"Ex - Count Unlabeled Graphs","description":{"content":"You are to generate a graph by the following procedure. *   Choose a simple undirected graph with $N$ unlabeled vertices. *   Write a positive integer at most $K$ in each vertex in the graph. Here, t","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc284_h"},"statements":[{"statement_type":"Markdown","content":"You are to generate a graph by the following procedure.\n\n*   Choose a simple undirected graph with $N$ unlabeled vertices.\n*   Write a positive integer at most $K$ in each vertex in the graph. Here, there must not be a positive integer at most $K$ that is not written in any vertex.\n\nFind the number of possible graphs that can be obtained, modulo $P$. ($P$ is a **prime**.)\nTwo graphs are considered the same if and only if one can label the vertices in each graph as $v_1, v_2, \\dots, v_N$ to satisfy the following conditions.\n\n*   For every $i$ such that $1 \\leq i \\leq N$, the numbers written in vertex $v_i$ in the two graphs are the same.\n*   For every $i$ and $j$ such that $1 \\leq i \\lt j \\leq N$, there is an edge between $v_i$ and $v_j$ in one of the graphs if and only if there is an edge between $v_i$ and $v_j$ in the other graph.\n\n## Constraints\n\n*   $1 \\leq K \\leq N \\leq 30$\n*   $10^8 \\leq P \\leq 10^9$\n*   $P$ is a prime.\n*   All values in the input are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$ $K$ $P$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc284_h","tags":[],"sample_group":[["3 1 998244353","4\n\nThe following four graphs satisfy the condition.\n![image](https://img.atcoder.jp/ghi/abc283h_43c4abe0e541b7ebeaa8db2854cece91caeca71f03f452ca13c11e82f85e3a56.png)"],["3 2 998244353","12\n\nThe following $12$ graphs satisfy the condition.\n![image](https://img.atcoder.jp/ghi/abc284h2_ca96b7cb451b0e495209e3e201576d278de3fb823e5d2404bbce5d9f704e3259.png)"],["5 5 998244353","1024"],["30 15 202300013","62712469"]],"created_at":"2026-03-03 11:01:13"}}