问题 B: Bloodline Counter

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 998 244 353.

The first line contains two integers n and k (3 ≤ k ≤ n ≤ 5×105 ), as explained in the problem statement.

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