Problem Description

Given a polynomial $A(x)$ of degree $n - 1$, find a polynomial $B(x)$ modulo $x^n$ such that $B(x) \equiv \text e^{A(x)}$. All coefficients are taken modulo $998244353$.

Input Format

The first line contains an integer $n$.

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

It is guaranteed that $a_0 = 0$.

Output Format

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

6
0 927384623 817976920 427326948 149643566 610586717

1 927384623 878326372 3882 273455637 998233543

Hint

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

Translated by ChatGPT 5