AMC 12 2014a Problem 16

The product $(8)(888\ldots 8)$, where the second factor has $k$ digits, is an integer whose digits have a sum of $1000$. What is $k$?

$\textbf{(A) }901 \textbf{(B) }911 \textbf{(C) }919 \textbf{(D) }991 \textbf{(E) }999$