9181: ABC204 —— F - Hanjo 2
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Description
We have a rectangular room that is $H$ meters long and $W$ meters wide.
We will fill this entire room with tatami (rectangular mats) that are $2$ meters long and $1$ meter wide, and hanjo (square mats) that are $1$ meter long and $1$ meter wide. Each tatami can be placed vertically or horizontally.
How many ways are there to fill the room?
We distinguish ways that match only after rotation or reflection.
Since the count can be enormous, find it modulo $998244353$.
We will fill this entire room with tatami (rectangular mats) that are $2$ meters long and $1$ meter wide, and hanjo (square mats) that are $1$ meter long and $1$ meter wide. Each tatami can be placed vertically or horizontally.
How many ways are there to fill the room?
We distinguish ways that match only after rotation or reflection.
Since the count can be enormous, find it modulo $998244353$.
Input
Input is given from Standard Input in the following format:
```
$H$ $W$
```
```
$H$ $W$
```
Output
Print the answer.
Constraints
- $1 \leq H \leq 6$
- $1 \leq W \leq 10^{12}$
- $1 \leq W \leq 10^{12}$
Sample 1 Input
2 2
Sample 1 Output
7
We have the following seven ways:
Sample 2 Input
3 3
Sample 2 Output
131
Sample 3 Input
5 100
Sample 3 Output
379944232
HINT
相同题目：ABC204。