Problem Statement

Kyoto City consists of $N \times M$ blocks arranged in a grid with $N$ rows running north to south and $M$ columns running east to west. The city is to be divided into several special wards.

Each special ward must be connected in the north, south, east, and west directions. That is, for any 2 blocks belonging to the same special ward, it must be possible to travel between them by moving only through blocks of that ward that are adjacent by sharing an edge.

When adjacent blocks belong to different special wards, a main road separating the blocks is built along their boundary. However, to prevent traffic congestion, no T-junction may be created in the interior of the grid. That is, at any intersection in the interior of the grid, the number of main roads connected to it must not be exactly $3$.

Find the total number of divisions into special wards satisfying the conditions, modulo $998244353$. Here, 2 ways of dividing are considered the same division if and only if, for any 2 blocks, whether those blocks belong to the same special ward agrees between them.

Input

The input is given from Standard Input in the following format.

$N$ $M$

• $1 \le N, M \le 3000$
• All input values are integers.

Output

Output the answer on $1$ line.

Sample

Sample 1

Input

2 2

Output

8

There are the following $8$ ways to divide the $2 \times 2$ blocks into special wards so that no T-junction is created in the interior.

For example, if the blocks are divided into 3 special wards as shown below, 3 main roads meet at the central intersection, creating a T-junction, so the conditions are not satisfied.

1 1

1

2026 529

996014394