408663: GYM103260 C Multiple?

Given an integer $$$n$$$, the sequence is called good if its elements are from $$$[1, n]$$$ and all its non-empty subsequences (not necessarily continuous) have sums not divisible by $$$n$$$.

Calculate the number of good sequences of length $$$n-k$$$ modulo $$$998\,244\,353$$$.

The only line of input contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le k \le n/4 < n < 998\,244\,353$$$).

Print one number — the answer to the problem.

4 1

2

9 2

48

222222222 222222

851798824