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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 $$$a_i+a_{i+1} \lt m$$$ ($$$1 \leq i \lt n$$$), and $$$a_1+a_n \lt m$$$, 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.

Note

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

Problems for Codeforces

Examples