Functionally, a Number theory problem

An increasing function \(f: \mathbb{N} ^{ \geq 0 } \rightarrow \mathbb{N} ^{ \geq 0 }\) satisfies \(f(2) = 7\) and

\[ f(mn) = f(m) + f(n) + f(m)f(n) \text{ for all } m, n \in \mathbb{N} ^{ \geq 0 }. \]

Find the remainder when \(f(2017)\) is divided by \(2017\).

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