AT_awtf2025_e Functional Graph

You are given integers $ N $ , $ C $ , and $ K $ . Find the number, modulo $ 998244353 $ , of length- $ N $ integer sequences $ x=(x_1,x_2,\ldots,x_N) $ satisfying the following conditions. - $ 1 \leq x_i \leq N $ ( $ 1 \leq i \leq N $ ). - Consider an undirected graph with $ N $ vertices numbered from $ 1 $ to $ N $ . This graph has $ N $ edges, and the $ i $ -th edge connects vertices $ i $ and $ x_i $ . Then, the number of connected components of the graph is exactly $ C $ . - The number of $ i $ satisfying $ i

The input is given from Standard Input in the following format: > $ N $ $ C $ $ K $

Output the answer.

### Sample Explanation 1 The following six sequences $ x $ satisfy the conditions: - $ x=(2,3,1) $ - $ x=(2,3,2) $ - $ x=(2,3,3) $ - $ x=(3,3,1) $ - $ x=(3,3,2) $ - $ x=(3,3,3) $ ### Constraints - $ 1 \leq N \leq 250000 $ - $ 1 \leq C \leq N $ - $ 0 \leq K \leq N-1 $ - All input values are integers.