AT_abc387_f [ABC387F] Count Arrays

You are given positive integers $ N $ , $ M $ , and a sequence $ A = (A_1, A_2, \dots, A_N) $ of length $ N $ , each element being an integer between $ 1 $ and $ N $ , inclusive. Find the number, modulo $ 998244353 $ , of sequences $ x = (x_1, x_2, \dots, x_N) $ of length $ N $ , each element being an integer between $ 1 $ and $ M $ , inclusive, that satisfy the following condition: - $ x_i \leq x_{A_i} $ for every $ i $ ( $ 1 \leq i \leq N $ ).

The input is given from Standard Input in the following format: > $ N $ $ M $ $ A_1 $ $ A_2 $ $ \dots $ $ A_N $

Print the answer.

### Sample Explanation 1 The sequences $ x=(1,1,1),(2,2,1),(2,2,2),(3,3,1),(3,3,2),(3,3,3) $ satisfy the condition. ### Constraints - $ 1 \leq N, M \leq 2025 $ - $ 1 \leq A_i \leq N $ - All input values are integers.