Problem Description

Given a polynomial $A(x)$ of degree $n - 1$, find a polynomial $B(x)$ modulo $x^n$ such that $B(x) \equiv \ln A(x)$.

All computations are done modulo $998244353$, and $a_i \in [0, 998244353) \cap \mathbb{Z}$.

Input Format

The first line contains an integer $n$.

The next line contains $n$ integers, which are the coefficients $a_0, a_1, \cdots, a_{n-1}$ of the polynomial in order.

It is guaranteed that $a_0 = 1$.

Output Format

Output $n$ integers, which are the coefficients $a_0, a_1, \cdots, a_{n-1}$ of the answer polynomial in order.

6
1 927384623 878326372 3882 273455637 998233543

0 927384623 817976920 427326948 149643566 610586717

Hint

For $100\%$ of the data, $n \le 10^5$.

Translated by ChatGPT 5