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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