P4721 [Template] Divide and Conquer FFT

It can also be solved using polynomial inversion.

Given a sequence $g_{1\dots n - 1}$, find the sequence $f_{0\dots n - 1}$. Here, $f_i=\sum_{j=1}^if_{i-j}g_j$, with the boundary condition $f_0=1$. Take the answer modulo $998244353$.

The first line contains an integer $n$. The second line contains $n-1$ integers $g_{1\dots n - 1}$.

Output one line with $n$ integers, representing the values of $f_{0\dots n - 1}$ modulo $998244353$.

Constraints: $2\leq n\leq 10^5$, $0\leq g_i