2016 is coming!

Algebra Level 5

\[ f(x) = x^{2016} + 2^3 x^{2015} + 3^3 x^{2014} + \cdots + 2016^3 x + 2017^3 \]

If \(a_{1}, a_{2},\ldots , a_{2016}\) are the roots of \(f(x) = 0\), then find the last three digits of the constant term of the polynomial whose roots are \(1 - a_{1}, 1 - a_{2}, \ldots , 1 - a_{2016}\).

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