410576: GYM104053 J Math Exam

There are many integer sequences in the world, and your mission is to find how many sequences are good.

An integer sequence $$$a_i$$$ of length $$$n$$$ is good if and only if all of these conditions holds:

• $$$\forall i \in [1,n], 4S_i = {a_i}^2 + 2a_i + 1$$$.
• $$$\forall i \in [1,n], |a_i| \le m$$$.

Where $$$S_i = \sum_{j=1}^i a_j$$$.

You will be given $$$n$$$ and $$$m$$$, and it is guaranteed that $$$m$$$ is odd.

Since the answer may be very large, you should calculate it modulo $$$998\, 244\, 353$$$.

The only line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n \le 10^7$$$, $$$1 \le m \leq 2n$$$, $$$m$$$ is odd).

Output a single integer — the number of good sequences meeting the constraints, modulo $$$998\, 244\, 353$$$.

9 13

124

500 999

195157058