In the shadowy aftermath of The Final Problem, Sherlock Holmes prepares for his greatest confrontation.Professor James Moriarty — the "Napoleon of Crime" — has assembled a vast and intricate network, threatening the very order of London. Holmes knows that even his unmatched intellect may not suffice this time. To defeat his greatest enemy, he must form a carefully balanced League of Detectives.

There are $$$n$$$ distinct investigative skills, numbered from $$$1$$$ to $$$n$$$, encompassing everything from forensic chemistry to cryptanalysis and disguise. Each detective is described by the set of skills they possess.The pool of candidates is limitless and contains every possible combination of skills.

Sherlock Holmes himself possesses exactly $$$k$$$ skills. To maintain command and coherence within the League, Holmes refuses to recruit anyone who surpasses him in expertise.

Furthermore, to ensure flawless cooperation against Moriarty's web, he imposes strict rules:Collaboration:

1. Any two detectives in the League must share at least one common skill, so that no pair is ever unable to collaborate.

2. Hierarchy: All selected detectives must possess the same number of skills, say $$$x$$$. This number must be at most $$$k$$$ ($$$1 \le x \le k$$$).

3. Uniqueness: No two detectives may have identical sets of skills.

Holmes wishes to recruit as many detectives as possible under these constraints, forming the largest League capable of bringing Moriarty to justice.

Determine the maximum possible size of the League.Since the answer may be large, output it modulo $$$998244353$$$.