Rearranging small sets for distinct partial sums

A conjecture of Graham (repeated by Erdos) asserts that for any set A Fₚ \0\, there is an ordering a₁, , a|₀| of the elements of A such that the partial sums a₁, a₁+a₂, , a₁+a₂++a|₀| are all distinct. We give a very short proof of this conjecture for sets A of size at most p/ p.