Multiplying First Quadrant Cosines: 2016 Of Them

Geometry Level 4

\[\prod \limits^{2016}_{n=1}\cos\left(\frac{n\pi }{2017}\right) \]

If the product above is equal to \( A^{-B} \), where \(A\) and \(B\) are positive integers with \(A\) is a prime number, find \(A + B\).

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