11324: [yosupo] Polynomial - Polynomial Root Finding (Mod 998244353)
[Creator : ]
Description
Given a polynomial $f(x) = \sum_{i=0}^Nf _ ix^i\in \mathbb{F} _ {998244353}[x]$ of degree $N$.
Find all $a\in \mathbb{F} _ {998244353}$ satisfying $f(a)=0$.
Find all $a\in \mathbb{F} _ {998244353}$ satisfying $f(a)=0$.
Input
$N$
$f_0$ $\cdots$ $f_N$
$f_0$ $\cdots$ $f_N$
Output
Print all $a$ satisfying $f(a)=0$ in the following format.
$n$
$a_0$ $\cdots$ $a_{n-1}$
$a_i$ should be printed as a non-negative integer less than $998244353$.
The order in which $a_i$ is output can be arbitrary.
Constraints
- $0\leq N\leq 4,000$
- $0\leq f_i < 998244353$
- $f_N\neq 0$
- $0\leq f_i < 998244353$
- $f_N\neq 0$
Sample 1 Input
2
6 998244348 1
Sample 1 Output
2
3 2
Sample 2 Input
2
3 0 1
Sample 2 Output
0
Sample 3 Input
5
1 5 10 10 5 1
Sample 3 Output
1
998244352
10
0 961956353 102657600 880974353 72368000 971311853 6327300 997299353 87000 998239853 100
10
1 3 0 2 4 5 9 8 7 6