201245: [AtCoder]ARC124 F - Chance Meeting

Problem Statement

Given is a grid with $H$ rows and $W$ columns. Let $(i, j)$ denote the square at the $i$-th row from the top and $j$-th column from the left.

Initially, a camel is on $(1, 1)$, and a cat is on $(H, 1)$.

You can send the following four kinds of orders.

• R: Move the camel on $(i, j)$ to $(i, j+1)$.
• D: Move the camel on $(i, j)$ to $(i+1, j)$.
• r: Move the cat on $(i, j)$ to $(i, j+1)$.
• u: Move the cat on $(i, j)$ to $(i-1, j)$.

A sequence of orders satisfying all of the four conditions below is said to be good. Find the number of good sequences of orders, modulo $998244353$.

1. The final position of the camel will be $(H, W)$.
2. The final position of the cat will be $(1, W)$.
3. The following will happen exactly once: the camel and the cat are on the same square after an order is processed.
4. Neither the camel nor the cat will leave the grid.

Constraints

• All values in input are integers.
• $2 \leq H,W \leq 2 \times 10^{5}$

Input

Input is given from Standard Input in the following format:

$H$ $W$

Output

Print the number of good sequences of orders, modulo $998244353$.

Sample Input 1

2 2

Sample Output 1

16

• The good sequences of orders include DRur, DurR, RruD, RDru, but not DRru, RRR.

Sample Input 2

200000 200000

Sample Output 2

412709667

• Be sure to print the count modulo $998244353$.