11335: [yosupo] Enumerative Combinatorics -Stirling Number of the Second Kind (Fixed K)
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Description
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 two integers $N,K$.
Calculate $S(n, K) \bmod 998244353$ for $K \le n \le N$.
$x^n = \sum_{k=0}^n S(n, k) x (x - 1) \cdots (x - (k - 1)).$
You are given two integers $N,K$.
Calculate $S(n, K) \bmod 998244353$ for $K \le n \le N$.
Input
$N$ $K$
Output
$S(K, K)$ $\cdots$ $S(N, K)$
Constraints
$0 \le K \le N \le 5\times 10^5$
Sample 1 Input
6 3
Sample 1 Output
1 6 25 90