Sum of the functions

$f(x, y) = \left(1 - \dfrac{1}{x}\right) \left(1 - \dfrac{1}{x + 1}\right) \left(1 - \dfrac{1}{x + 2}\right) ... \left(1 - \dfrac{1}{y}\right)$

Function $f(x)$ is defined as above, where $x$ and $y$ are integers such that $1 < x \leq y$ .

If $S = f(2, 2014) + f(3, 2014) + f(4, 2014) +...+ f(2013, 2014) = \dfrac ab$ , where $a$ and $b$ are coprime positive integers, what is the last three digits of $a + b$ ?