Problem Statement

There is a shogi (Japanese chess) board with $H$ rows and $W$ columns, and one knight piece. The square at the $i$-th row from the top and $j$-th column from the left of the board is represented as $(i-1, j-1)$. (Note that the values are shifted by $1$.) This board is a torus, meaning the top and bottom are connected, and the left and right are connected. A knight at $(i, j)$ can move to $((i-2) \bmod H, (j-1) \bmod W)$ or $((i-2) \bmod H, (j+1) \bmod W)$. (Note that this is different from the knight in Standard chess.)

Moving the knight on the board to satisfy the following condition is called a tour.

• Initially, place the knight at $(0, 0)$. Then, move the knight $H \times W$ times so that the knight visits every square exactly once. Finally, the knight returns to $(0, 0)$.

Find the number of tours modulo $998244353$. Two tours are considered different if and only if there exists an integer $i$ $(1 \leq i \leq H\times W)$ such that the destination of the $i$-th move is different.

Constraints

• $3 \leq H \leq 2 \times 10^5$
• $3 \leq W \leq 2 \times 10^5$
• All input values are integers.

Input

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

H W

Output

Output the number of tours modulo $998244353$.