AT_fps_24_h ジャンプ

On a 2D coordinate plane, a piece is placed at $ (0, 0) $ . You may perform the following operation any number of times (including zero): - Choose an integer pair $ (a, b) $ such that $ 0 \leq a \leq 1 $ , $ 0 \leq b $ , and $ (a, b) \neq (0, 0) $ . - If the current position of the piece is $ (x, y) $ , move it to $ (x+a, y+b) $ . Find the number of operation sequences that result in the piece being at $ (N, M) $ after all operations, and output the answer modulo $ 998244353 $ .

The input is given from standard input in the following format: > $ N $ $ M $

Print the answer.

### Sample Explanation 1 For each valid operation sequence, the visited coordinates are as follows (5 possibilities): - $ (0, 0) \to (0, 1) \to (1, 1) \to (2, 1) $ - $ (0, 0) \to (1, 0) \to (1, 1) \to (2, 1) $ - $ (0, 0) \to (1, 0) \to (2, 0) \to (2, 1) $ - $ (0, 0) \to (1, 0) \to (2, 1) $ - $ (0, 0) \to (1, 1) \to (2, 1) $ ### Constraints - $ 1 \leq N \leq 2 \times 10^5 $ - $ 1 \leq M \leq 2 \times 10^5 $ - All input values are integers