J. Math Exam
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$998\, 244\, 353$$$.

Input

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

Output

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

Examples
Input
9 13
Output
124
Input
500 999
Output
195157058