VMO 1969 Problem 1

A graph $G$ has $n + k$ vertices. Let $A$ be a subset of $n$ vertices of the graph $G$ , and $B$ be a subset of other $k$ vertices. Each vertex of $A$ is joined to at least $k - p$ vertices of $B$ . Prove that if $np < k$ then there is a vertex in $B$ that can be joined to all vertices of $A$ .