Problem11335--[yosupo] Enumerative Combinatorics -Stirling Number of the Second Kind (Fixed K)

11335: [yosupo] Enumerative Combinatorics -Stirling Number of the Second Kind (Fixed K)

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Time Limit : 2.000 sec  Memory Limit : 512 MiB

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 $K \le n \le N$.

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

HINT

Yosupo.

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