Score : $2000$ points

Problem Statement

There are positive integers $N$ and $M$.

A binary string $s$ is called good if all of the followings are satisfied:

• $s$ is non-empty.
• The number of 1s in $s$ is a multiple of $N$.
• The number of 0s in $s$ is a multiple of $M$.

A good string is called perfect if it doesn't contain shorter good (contiguous) substrings. For example, if $N = 3$ and $M = 2$, then strings 111, 00 and 10101 are perfect, but 0000 and 11001 are not.

One can show that for any $N, M$ the number of perfect strings is finite. Find this number modulo $998\,244\,353$.

Constraints

• $1 \leq N, M \leq 40$
• All values in the input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$

Output

Print the answer.

2 2

4

The perfect strings are 00, 0101, 1010, 11.

3 2

7

The perfect strings are 00, 01011, 01101, 10101, 10110, 11010, 111.

23 35

212685109