Logs of this year

Algebra Level 3

\[\text{A} = \log_{2016} \log_{2015} \cdots \log_3 \log_2 2^{3^{{.}^{{.}^{{.}^{{2015}^{2016}}}}}} \\ \text{or}\\ \text{B} = \log_2 \log_3 \cdots \log_{2015} \log_{2016} {2016}^{{2015}^{{.}^{{.}^{{.}^{{3}^{2}}}}}}\]

Which of the above expressions is greater?

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