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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