P5264 Polynomial Trigonometric Functions

Given a polynomial $A(x)$ of degree $n-1$, find a polynomial $F(x)$ modulo $x^n$ such that $F(x)\equiv\sin{A(x)}$ or $F(x)\equiv\cos{A(x)}$. All operations are performed modulo $998244353$.

The first line contains **two** integers $n,type$. If $type=0$, compute $\sin$; if $type=1$, compute $\cos$. The second line contains $n$ integers, which are the coefficients $a_0,a_1,\cdots,a_{n-1}$ of the polynomial. It is guaranteed that $a_0=0$.

Output one line with $n$ integers, representing the coefficients $f_0,f_1,\cdots,f_{n-1}$ of the resulting polynomial.

Constraints for $100\%$ of the testdata: $n\leq10^5$, $a_i\in[0,998244352]\cap\mathbb{Z}$. For the first $5$ test points, $type=0$; for the last $5$ test points, $type=1$. Translated by ChatGPT 5