# Stirling Number of the Second Kind

AC一覧

## Problem Statement問題文

The Stirling numbers of the second kind $S(n, k)$ are defined as the coefficients in the identity $$x^n = \sum_{k=0}^n S(n, k) x (x - 1) \cdots (x - (k - 1)).$$

You are given an integer $N$. Calculate $S(N, k) \bmod 998{,}244{,}353$ for $0 \le k \le N$.

## Constraints制約

• $0 \le N \le 500{,}000$

## Input入力

$N$


## Output出力

$S(N, 0)$ $\cdots$ $S(N, N)$


## Sampleサンプル

### # 1

5

0 1 15 25 10 1


Timelimit: 10 secs

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