CF1580F.Problems for Codeforces

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 $a_i \neq b_i$ .

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

Print a single integer — the number of different plans.

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 $a_1+a_n \geq m$ .