BALTIC-WAY 2002 Problem 2

Let $a, b, c, d$ be real numbers such that

$$\begin{aligned} a+b+c+d & =-2 \\ a b+a c+a d+b c+b d+c d & =0 \end{aligned}$$

Prove that at least one of the numbers $a, b, c, d$ is not greater than -1 .