F. Problems for Codeforces
time limit per test
8 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

XYMXYM and CQXYM will prepare $n$ problems for Codeforces. The difficulty of the problem $i$ will be an integer $a_i$, where $a_i \geq 0$. The difficulty of the problems must satisfy $a_i+a_{i+1}<m$ ($1 \leq i < n$), and $a_1+a_n<m$, where $m$ is a fixed integer. XYMXYM wants to know how many plans of the difficulty of the problems there are modulo $998\,244\,353$.

Two plans of difficulty $a$ and $b$ are different only if there is an integer $i$ ($1 \leq i \leq n$) satisfying $a_i \neq b_i$.

Input

A single line contains two integers $n$ and $m$ ($2 \leq n \leq 50\,000$, $1 \leq m \leq 10^9$).

Output

Print a single integer — the number of different plans.

Examples
Input
3 2

Output
4

Input
5 9

Output
8105

Input
21038 3942834

Output
338529212

Note

In the first test case, the valid $a$ are: $[0,0,0]$, $[0,0,1]$, $[0,1,0]$, $[1,0,0]$.

$[1,0,1]$ is invalid since $a_1+a_n \geq m$.