{"raw_statement":[{"iden":"problem statement","content":"You are given integers $N$, $C$, and $K$. Find the number, modulo $998244353$, of length-$N$ integer sequences $x=(x_1,x_2,\\ldots,x_N)$ satisfying the following conditions.\n\n*   $1 \\leq x_i \\leq N$ ($1 \\leq i \\leq N$).\n*   Consider an undirected graph with $N$ vertices numbered from $1$ to $N$. This graph has $N$ edges, and the $i$\\-th edge connects vertices $i$ and $x_i$. Then, the number of connected components of the graph is exactly $C$.\n*   The number of $i$ satisfying $i<x_i$ is exactly $K$."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 250000$\n*   $1 \\leq C \\leq N$\n*   $0 \\leq K \\leq N-1$\n*   All input values are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $C$ $K$"},{"iden":"sample input 1","content":"3 1 2"},{"iden":"sample output 1","content":"6\n\nThe following six sequences $x$ satisfy the conditions:\n\n*   $x=(2,3,1)$\n*   $x=(2,3,2)$\n*   $x=(2,3,3)$\n*   $x=(3,3,1)$\n*   $x=(3,3,2)$\n*   $x=(3,3,3)$"},{"iden":"sample input 2","content":"3 2 2"},{"iden":"sample output 2","content":"0"},{"iden":"sample input 3","content":"6 3 0"},{"iden":"sample output 3","content":"225"},{"iden":"sample input 4","content":"20 4 7"},{"iden":"sample output 4","content":"476087626"},{"iden":"sample input 5","content":"250000 2025 125000"},{"iden":"sample output 5","content":"410390562"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}