Yay for 2014! #6

Let $r_{1}, r_{2}, ..., r_{2014}$ be the complex roots, not all necessarily distinct, of the polynomial $x^{2014}+2014x^{2013}-1$ . If

$S = \sum_{n=1}^{2014}\sum_{k=1}^{2014}r_{k}^{n},$

and $\frac{2015}{2014}S = a^{2014} + b$ , for some positive integers $a$ and $b$ such that $a$ is as large as possible, find the units digit of $a + b + 2014.$

This problem is part of the set Yay for 2014! .