A2 Sean $u_1, u_2, \dots, u_{2019}$ números reales que satisfacen \[u_{1}+u_{2}+\cdots+u_{2019}=0 \quad \text { and } \quad u_{1}^{2}+u_{2}^{2}+\cdots+u_{2019}^{2}=1.\] Sea $a=\min \left(u_{1}, u_{2}, \ldots, u_{2019}\right)$ y $b=\max \left(u_{1}, u_{2}, \ldots, u_{2019}\right)$ . Demuestre que \[ a b \leqslant-\frac{1}{2019}. \] y-is-the-best-_