AT_fps_24_d 数列 2

Consider integer sequences $ A=(a_1,a_2,\dots,a_N) $ of length $ N $ , where each element is a non-negative integer not greater than $ M $ . Count how many such sequences satisfy the following condition, and output the result modulo $ 998244353 $ . - Let $ B=(b_1,b_2,\dots,b_N) $ be the sequence obtained by sorting $ A $ in ascending order. For every $ i $ such that $ 1 \leq i \leq N-1 $ , the parity of $ b_i $ and $ b_{i+1} $ must be different.

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

Print the answer.

### Sample Explanation 1 There are $ 8 $ sequences that satisfy the condition: - $ (0,1) $ - $ (0,3) $ - $ (1,0) $ - $ (1,2) $ - $ (2,1) $ - $ (2,3) $ - $ (3,0) $ - $ (3,2) $ ### Constraints - $ 1 \leq N \leq 2 \times 10^5 $ - $ 1 \leq M \leq 2 \times 10^5 $ - $ N, M $ are integers