AMC 12B 2011 Problem 17

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

Answer Choices
A. 16,081
B. 16,089
C. 18,089
D. 18,098
E. 18,099