11292: [yosupo] Polynomial - Log 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 $a_0 = 1$.
Calculate the first $N$ terms of $\log(f(x)) = \sum_{i=0}^{\infty} b_i x^i$.
In other words, find $g(x) = \sum_{i=0}^{N-1} b_i x^i \in \mathbb{Q}[[x]]$ such that $b_0 = 0$ and
$f(x) \equiv \sum_{k=0}^{N-1} \frac{g(x)^k}{k!} \pmod{x^N}.$
Print the coefficients modulo $998244353$.
Calculate the first $N$ terms of $\log(f(x)) = \sum_{i=0}^{\infty} b_i x^i$.
In other words, find $g(x) = \sum_{i=0}^{N-1} b_i x^i \in \mathbb{Q}[[x]]$ such that $b_0 = 0$ and
$f(x) \equiv \sum_{k=0}^{N-1} \frac{g(x)^k}{k!} \pmod{x^N}.$
Print the coefficients modulo $998244353$.
Input
$N$
$a_0$ $a_1$ $\cdots$ $a_{N - 1}$
$a_0$ $a_1$ $\cdots$ $a_{N - 1}$
Output
$b_0$ $b_1$ $\cdots$ $b_{N - 1}$
Constraints
- $1 \leq N \leq 5\times 10^5$
- $0 \leq a_i < 998244353$
- $a_0 = 1$
- $0 \leq a_i < 998244353$
- $a_0 = 1$
Sample 1 Input
5
1 1 499122179 166374064 291154613
Sample 1 Output
0 1 2 3 4