$\begin{aligned} A &= &(1+a_2)^2 (1+a_3)^3 \cdots (1+a_{2016})^{2016} \\ B &=& 2016^{2016} \end{aligned}$

Given that $a_2, a_3, \ldots, a_{2016}$ are non-negative real numbers such that their product is 1, and let $A$ and $B$ as described above.

Which of the following equation/inequation must be true?