IrMO 2016 Problem 5

Let $a_1, a_2, ..., a_m$ be positive integers, none of which is equal to $10$ , such that $a_1 + a_2 + ...+ a_m = 10m$ . Prove that $(a_1a_2a_3 \cdot ...\cdot a_m)^{1/m} \le 3\sqrt{11}$ .