TH-TMO 2013 Problem 8

Let $p(x) = x^{2013} + a_{2012}x^{2012} + a_{2011}x^{2011} +...+ a_1x + a_0$ be a polynomial with real coefficients with roots $- b_{1006}, - b_{1005}, ... , -b_1, 0, b_1, ... , b_{1005}, b_{1006}$ , where $b_1, b_2, ... , b_{1006}$ are positive reals with product $1$ . Show that $a_3a_{2011} \le 1012036$