PASCAL 2014 Problem 25

Suppose that \displaystyle\frac{2009}{2014}+\frac{2019}{n}=\frac ab where a,b and n are positive integers with \displaystyle\frac ab in lowest terms. What is the sum of the digits of the smallest positive integer n for which a is a multiple of 1004?

Answer Choices
A. 16
B. 17
C. 14
D. 20
E. 21