AMC 12 2011b Problem 17

Let $f(x) = 10^{10x}, g(x) = \log_{10}\left(\frac{x}{10}\right), h_1(x) = g(f(x))$, and $h_n(x) = h_1(h_{n-1}(x))$ for integers $n \geq 2$. What is the sum of the digits of $h_{2011}(1)$?

\textbf{(A)}\ 16081 \textbf{(B)}\ 16089 \textbf{(C)}\ 18089 \textbf{(D)}\ 18098 \textbf{(E)}\ 18099