AMC 12 2014a Problem 23

The fraction $$\dfrac1{99^2}=0.\overline{b_{n-1}b_{n-2}\ldots b_2b_1b_0},$$ where $n$ is the length of the period of the repeating decimal expansion. What is the sum $b_0+b_1+\cdots+b_{n-1}$?

$\textbf{(A) }874 \textbf{(B) }883 \textbf{(C) }887 \textbf{(D) }891 \textbf{(E) }892$