AMC 12 2018b Problem 18

A function $f$ is defined recursively by $f(1)=f(2)=1$ and $$f(n)=f(n-1)-f(n-2)+n$$for all integers $n \geq 3$. What is $f(2018)$?

$\textbf{(A) } 2016 \textbf{(B) } 2017 \textbf{(C) } 2018 \textbf{(D) } 2019 \textbf{(E) } 2020$