{"problem":{"name":"Biconnected Graph","description":{"content":"You are given an integer $N$ and a prime $P$. Count the number, modulo $P$, of undirected connected graphs $G$ of $N$ vertices numbered $1$ to $N$ that satisfy the following condition: *   There are ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":3000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"agc067_e"},"statements":[{"statement_type":"Markdown","content":"You are given an integer $N$ and a prime $P$.\nCount the number, modulo $P$, of undirected connected graphs $G$ of $N$ vertices numbered $1$ to $N$ that satisfy the following condition:\n\n*   There are no self-loops in $G$. Note that multiple edges are allowed.\n*   For all edges $(u,v)$ in $G$, if we delete $(u,v)$ from $G$, $G$ remains connected. In other words, $G$ is edge-biconnected.\n*   For all edges $(u,v)$ in $G$, if we delete $(u,v)$ from $G$, $G$ is no longer edge-biconnected.\n\nTwo graphs are considered different if and only if there exists a pair of distinct vertices $(u,v)$ such that the numbers of edges connecting $u$ and $v$ in the two graphs are different.\n\n## Constraints\n\n*   $2 \\le N \\le 50$\n*   $10^9<P<1.01\\times 10^9$\n*   $P$ is prime.\n*   All input values are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $P$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"agc067_e","tags":[],"sample_group":[["2 1005976817","1"],["5 1000837403","372"],["10 1001160547","789846604"],["20 1006779551","888612770"]],"created_at":"2026-03-03 11:01:14"}}