Editorial for Another Contest 4 Problem 9 - Fast Fourier Transform!

Remember to use this editorial only when stuck, and not to copy-paste code from it. Please be respectful to the problem author and editorialist.
Submitting an official solution before solving the problem yourself is a bannable offence.

The function to implement is a vector of the first $n$ ~n~ factorials, modulo $998\,244\,353$ ~998\,244\,353~, as motivated by the problem statement and problem title.