3433 . [模板題] Exp of Formal Power Series
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Description
You are given a formal power series $f(x) = \sum_ {i=0}^ {N-1} a_ i x^ i \in \mathbb{Q}[[x]]$ with $a_ 0 = 0$.
Calculate the first $N$ terms of $\exp(f(x)) = \sum_ {i=0}^ {\infty} b_ i x^ i$.
In other words, find $g(x) = \sum_ {i=0}^ {N-1} b_ i x^ i \in \mathbb{Q}[[x]]$ such that
$$g(x) \equiv \sum_ {k=0}^ {N-1} \frac{f(x)^ k}{k!} \pmod{x^ N}.$$
Print the coefficients modulo $998244353$.
Input Format
$N$
$a_ 0$ $a_ 1$ $\cdots$ $a_ {N - 1}$
Output Format
$b_ 0$ $b_ 1$ $\cdots$ $b_ {N - 1}$
Sample Input 1
5 0 1 2 3 4
Sample Output 1
1 1 499122179 166374064 291154613
Hints
- $1 \leq N \leq 5 \times 10^ {5}$
- $0 \leq a_ i < 998244353$
- $a_ 0 = 0$
Problem Source
Subtasks
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