8861: [yosupo] Enumerative Combinatorics - Stirling Number of the First Kind
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Description
The signed Stirling numbers of the first kind $s(n, k)$ are defined as the coefficients in the identity
$x (x - 1) \cdots (x - (n - 1)) = \sum_{k=0}^n s(n, k) x^k.$
You are given an integer $N$.
Calculate $s(N, k) \bmod 998244353$ for $0 \le k \le N$.
$x (x - 1) \cdots (x - (n - 1)) = \sum_{k=0}^n s(n, k) x^k.$
You are given an integer $N$.
Calculate $s(N, k) \bmod 998244353$ for $0 \le k \le N$.
Input
$N$
Constraints
$0 \le N \le 500,000$
Sample 1 Input
5
Sample 1 Output
0 24 998244303 35 998244343 1