PL-OM 2010 Problem 5

Prime number $p>3$ is congruent to $2$ modulo $3$ . Let $a_k = k^2 + k +1$ for $k=1, 2, \ldots, p-1$ . Prove that product $a_1a_2\ldots a_{p-1}$ is congruent to $3$ modulo $p$ .