Let $S$ be the set of all subsets of $\{2,3,\ldots,2016\}$ with size $1007$, and for a nonempty set $T$ of numbers, let $f(T)$ be the product of the elements in $T$. Determine the remainder when \[ \sum_{T\in S}\left(f(T)-f(T)^{-1}\right)^2\] is divided by $2017$. Note: For $b$ relatively prime to $2017$, $b^{-1}$ is the unique positive integer less than $2017$ for which $2017$ divides $bb^{-1} -1$.

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