Fraction Tower

Algebra Level 3

Let us define a fraction tower be fraction like this:       8        4  21\dfrac{\;\;\;8\;\;\;}{\dfrac{\;4\;}{\dfrac{2}{1}}}

That is, when we look from top to bottom, the fraction line is shorter and shorter and the numbers are decreasing power of 2.

What is the value of fraction tower with 220162^{2016} at the top?
Let the answer be 2A2^A, enter AA as your answer.

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