Problem11334--[yosupo] Enumerative Combinatorics -Stirling Number of the First Kind (Fixed K)

11334: [yosupo] Enumerative Combinatorics -Stirling Number of the First Kind (Fixed K)

[Creator : ]
Time Limit : 1.000 sec  Memory Limit : 512 MiB

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 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 998244347 35 998244128

HINT

Yosupo.

Source/Category