JBMO-SL 2005 A1

Let $a, b, c, d, e$ be real numbers such that $a+b+c+d+e=0$. Let, also $A=a b+b c+c d+d e+e a$ and $B=a c+c e+e b+b d+d a$.

Show that

$$2005 A+B \leq 0 \text { or } A+2005 B \leq 0$$