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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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