问题 B: Bloodline Counter

链接：https://ac.nowcoder.com/acm/contest/57362/B
来源：牛客网
A tournament is a directed graph obtained by assigning a direction for each edge in an undirected complete graph.

We say a tournament is grand, if and only if the largest directed cycle in the tournament contains exactly $k$ vertices.

Please count the number of different labeled grand tournaments of $n$ vertices, modulo $998244353$

The first line contains two integers $n$ and $k$ (3≤k≤n≤5×1053\le k \le n \le 5 \times 10^53≤k≤n≤5×105), as explained in the problem statement.

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