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문제

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 $998\,244\,353$.

입력

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

출력

Print one number --- the answer to the problem.

예제 입력 1

4 1

예제 출력 1

2

예제 입력 2

9 2

예제 출력 2

48

예제 입력 3

222222222 222222

예제 출력 3

851798824