AMC 10 2014a Problem 20

The product $(8)(888\dots8)$, where the second factor has $k$ digits, is an integer whose digits have a sum of $1000$. What is $k$? $\textbf{(A)}\ 901 \textbf{(B)}\ 911 \textbf{(C)}\ 919 \textbf{(D)}\ 991 \textbf{(E)}\ 999$