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.

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

Input

Input is given from Standard Input in the following format:
H W

Output

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

Constraints

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

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.

见题面 Input 部分

见题面 Output 部分