From x to y

Level pending

Let $$x$$ and $$y$$ be integers such that $$1<x\leq y$$, and the function $$f$$ be defined as

$f(x,y)=\displaystyle\prod_{k=x}^y \left(1-\frac{1}{k}\right)$

If $$S=\displaystyle\sum_{k=2}^{2014} {f(k, 2014)}$$, then the exact value of $$S$$ can be expressed as a mixed number $$a\frac{b}{c}$$, where $$a$$ is a positive integer and $$b$$ and $$c$$ are positive coprime integers. What is the value of $$a-10b-10c$$?

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