P5245 [Template] Fast Polynomial Exponentiation

[Enhanced version link](https://www.luogu.com.cn/problem/P5273) This is a template problem, with no background.

Given a polynomial $A(x)$ of degree $n-1$, find a polynomial $B(x)$ modulo $x^n$ such that $B(x) \equiv (A(x))^k \ (\bmod\ x^n)$. The coefficients of the polynomials are computed modulo $998244353$.

The first line contains two integers $n, k$. The next line contains $n$ integers, representing the coefficients of $A(x)$ in order: $a_0, a_1, ..., a_{n-1}$.

Output $n$ integers, representing the first $n$ coefficients of $B(x)$ in order: $b_0, b_1, ..., b_{n-1}$. Each coefficient should be the smallest non-negative integer modulo $998244353$.

For $100\%$ of the testdata, $1 < n \leq 10^5$, $0 < k \leq 10^{10^5}$, $a_i \in [0,998244352]$, and $a_0 = 1$. Translated by ChatGPT 5