AT_awtf2025_d BFS-ordered Tree

You are given an integer $ N $ . We call a rooted tree $ T $ satisfying the following conditions a **BFS-ordered tree**. - $ T $ is a rooted tree with $ N $ vertices numbered from $ 1 $ to $ N $ . - The root is vertex $ 1 $ . - Let vertex $ p_i $ be the parent of each vertex $ i $ ( $ 2 \leq i \leq N $ ). Then, $ p_2 \leq p_3 \leq \cdots \leq p_N $ holds. For each $ d=1,2,\ldots,(N-1) $ , find the number, modulo $ 998244353 $ , of BFS-ordered trees $ T $ satisfying the following condition. - The distance between vertices $ (N-1) $ and $ N $ in $ T $ is exactly $ d $ . More precisely, when considering $ T $ as an undirected tree and the path connecting vertices $ (N-1) $ and $ N $ , the number of edges in that path is exactly $ d $ .

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

Output $ N-1 $ lines. The $ i $ -th line should contain the answer for $ d=i $ .

### Constraints - $ 2 \leq N \leq 10^6 $ - All input values are integers.