P5383 Convert an Ordinary Polynomial to a Falling-Factorial Polynomial

This is a template problem.

Given an ordinary polynomial $F(x)=\displaystyle\sum_{i=0}^{n-1}a_ix^{i}$. Find a falling-factorial polynomial $G(x)=\displaystyle\sum_{i=0}^{n-1}b_ix^{\underline{i}}$. Such that $G(x)=F(x)$. All operations are performed modulo $998244353$.

The first line contains a positive integer $n$, as described above. The second line contains $n$ numbers. The $i$-th number represents $a_{i-1}$.

Output one line with $n$ numbers. The $i$-th number is $b_{i-1}$.

For all testdata, $a_i\in\lbrack0,998244353)$. This problem has a total of $10$ subtasks. Among them, $3$ subtasks have $n=2000$. The other $7$ subtasks have $n=10^5$. Translated by ChatGPT 5