Let's say we have a polynomial $$$P(x)$$$ in the field modulo $$$(10^9+7)$$$
For $$$n=10^5$$$ obviously we can't generate the whole polynomial explicitly. But I think maybe we can solve the following problems
- Find the coefficient of $$$x^k$$$ in $$$P(x)$$$
- Find the polynomial $$$P(x)\%x^k$$$
I don't how to solve them efficiently. That's why I am asking you guys. How efficiently can you solve the problems for some $$$k$$$?