A large gap in a dilate of a set

Let $A\subset {\mathbb{F}}_p$ with $\mathrm{\mid }A\mathrm{\mid }>1$. We show there is a $d \in $\mathbb{F}$_p^{\times}$suchthat$d \cdot A$containsagapofsizeatleast$2p/ |A| - 2 $.