{"problem":{"name":"Unbranched","description":{"content":"Find the number of graphs with $N$ labeled vertices and $M$ unlabeled edges, not necessarily simple or connected, that satisfy the following conditions, modulo $(10^9+7)$: *   There is no self-loop; ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc180_f"},"statements":[{"statement_type":"Markdown","content":"Find the number of graphs with $N$ labeled vertices and $M$ unlabeled edges, not necessarily simple or connected, that satisfy the following conditions, modulo $(10^9+7)$:\n\n*   There is no self-loop;\n*   The degree of every vertex is at most $2$;\n*   The maximum of the sizes of the connected components is exactly $L$.\n\n## Constraints\n\n*   $2 \\leq N \\leq 300$\n*   $1\\leq M \\leq N$\n*   $1 \\leq L \\leq N$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $M$ $L$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc180_f","tags":[],"sample_group":[["3 2 3","3\n\nWhen the vertices are labeled $1$ through $N$, the following three graphs satisfy the condition:\n\n*   The graph with edges $1-2$ and $2-3$;\n*   The graph with edges $1-2$ and $1-3$;\n*   The graph with edges $1-3$ and $2-3$."],["4 3 2","6"],["300 290 140","211917445"]],"created_at":"2026-03-03 11:01:14"}}