# Relentless reciprocals

The equation

$$\displaystyle \frac{1}{x_1}+\frac{1}{x_2}+...+\frac{1}{x_{2014}}+\frac{1}{x_1.x_2.....x_{2014}}=1$$

has a unique solution in positive integers, where $$x_1<x_2<...<x_{2014}$$

Find $$x_{2014}$$ modulo $$5 \times 7 \times 13$$.

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