11319: [yosupo] Polynomial - Polynomial Taylor Shift
[Creator : ]
Description
A Polynomial $f(x) = \sum_{i=0}^{N-1} a_ix^i \in \mathbb{Z}[x]$ and an integer $c$ is given.
Compute the sequence $b_0, b_1, \ldots, b_{N-1}$ satisfying $f(x+c) = \sum_{i=0}^{N-1}b_ix^i$, and print it modulo $998244353$.
Compute the sequence $b_0, b_1, \ldots, b_{N-1}$ satisfying $f(x+c) = \sum_{i=0}^{N-1}b_ix^i$, and print it modulo $998244353$.
Input
$N$ $c$
$a_0$ $a_1$ ... $a_{N-1}$
$a_0$ $a_1$ ... $a_{N-1}$
Output
$b_0$ $b_1$ ... $b_{N - 1}$
Constraints
- $1 \leq N \leq 2^{19}$
- $0 \leq c, a_i < 998244353$
- $0 \leq c, a_i < 998244353$
Sample 1 Input
5 3
1 2 3 4 5
Sample 1 Output
547 668 309 64 5
Sample 2 Input
2 10000000
10000000 10000000
Sample 2 Output
881938225 10000000