Find the smallest positive integer $k$ such that there exist positive integers $M, O > 1$ satisfying:
\[
 (O \cdot M \cdot O)^k = (O \cdot M) \cdot \underbrace{(N \cdot O \cdot M) \cdot (N \cdot O \cdot M) \cdot \ldots \cdot (N \cdot O \cdot M)}_{2016 \text{\ (N \cdot O \cdot M)s}},
\]
where $N = O^M$.

Let's think step by step and output the final answer within \boxed{}.
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