{"raw_statement":[{"iden":"problem statement","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 $L$."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 300$\n*   $1\\leq M \\leq N$\n*   $1 \\leq L \\leq N$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $M$ $L$"},{"iden":"sample input 1","content":"3 2 3"},{"iden":"sample output 1","content":"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 $2-3$."},{"iden":"sample input 2","content":"4 3 2"},{"iden":"sample output 2","content":"6"},{"iden":"sample input 3","content":"300 290 140"},{"iden":"sample output 3","content":"211917445"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}