Background

This is a template problem.

Problem Description

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 $998244353$.

Input Format

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 Format

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

3
1 1 1

1 2 1

Hint

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