AT_fps_24_e 数列 3

Consider integer sequences $ A = (a_1,a_2,\dots,a_N) $ of length $ N $ , where each element is a positive integer not greater than $ M $ . Count how many such sequences satisfy the following condition, and output the result modulo $ 998244353 $ . - For every integer $ m $ such that $ 1 \leq m \leq M $ , the number of times $ m $ appears in $ A $ is at most $ m $ .

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: - $ (1, 2) $ - $ (1, 3) $ - $ (2, 1) $ - $ (2, 2) $ - $ (2, 3) $ - $ (3, 1) $ - $ (3, 2) $ - $ (3, 3) $ ### Constraints - $ 1 \leq N \leq 300 $ - $ 1 \leq M \leq 300 $ - $ N, M $ are integers