Let $\mathbf{M} = \begin{pmatrix} 2 & 1 \\ -1 & 4 \end{pmatrix},$ and let \[\mathbf{M}^{2016} = \begin{pmatrix} a & b \\ c & d \end{pmatrix}.\]Find $d.$ Express your answer in the form $m \cdot p^n,$ where $m,$ $n,$ $p$ are positive integers, $p$ is prime, and $m$ is not divisible by $p.$
