2014 AMC 10A Problem 20

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

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