2014 AMC 12A 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\qquad \textbf{(B) }911\qquad \textbf{(C) }919\qquad \textbf{(D) }991\qquad \textbf{(E) }999\qquad

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.