# Base 2014 Termination

Suppose a rational number $$r<1$$ can be expressed as $$r=\dfrac{1}{n}$$ for some positive integer $$n$$. The sum of all possible values of $$r$$ such that the base $$2014$$ representation of $$r$$ is a terminating decimal can be expressed as $$\dfrac{p}{q}$$ for coprime positive integers $$p,q$$. What is the value of $$p$$?

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