|시간 제한||메모리 제한||제출||정답||맞은 사람||정답 비율|
|2 초||512 MB||0||0||0||0.000%|
Consider strings consisting of the brackets '
(' and '
The regular bracket sequences are the strings which can be obtained by the following rules:
)is a regular bracket sequence.
You are given $N$ boxes numbered $1, 2, \ldots, N$, and also two integers, $M$ and $K$. Your task is to put exactly one regular bracket sequence in each of $N$ boxes such that the following conditions are met:
(' brackets in all $N$ boxes is equal to $M$.
Count the number of different ways to do that. Two distributions are considered different if there exists a number $i$ such that box $i$ contains different regular bracket sequences in those distributions.
Because the answer may be very large, print the answer modulo $998\,244\,353$.
The input contains one line with three integers $N$, $M$, and $K$ in it ($1 \le M, N \le 10^6$, $1 \le K \le M$).
Print the answer modulo $998\,244\,353$.
2 2 1
1 1 1
24 120 30
For the first example, the following distributions meet the conditions:
So, the answer is $4$.