# That's huge!

Algebra Level 5

Let $${ x }_{ 1 },...,{ x }_{ 2016 }$$ be positive reals so that $${ x }_{ 1 }+...+{ x }_{ 2016 }=1$$. The minimum value of $(\frac { 1 }{ { x }_{ 1 } } +2014)...(\frac { 1 }{ { x }_{ 2016 } } +2014)$

can be expressed as $$a ^b$$, where $$a$$ and $$b$$ are positive integers, and $$b$$ is as large as possible. Find $$a + b$$.

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