# Expand the expression? No way!

Algebra Level 5

Let $$f(x)$$ denote a monic $$2015^{\text{th}}$$ degree polynomial with integer coefficients and with roots $$r_1, r_2, \ldots , r_{2015}$$

And $$S_n = (-1)^n n^3$$, where $$S_n$$ denote the $$n^{\text{th}}$$ symmetric sum of numbers $$r_1, r_2, \ldots , r_{2015}$$.

What is the last three digits of

$\left| \prod_{k=1}^{2015} (r_k + 1) \right| ?$

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