  In this paper we show that for any $k\geq2$, there exist two universal
constants $C_k,D_k>0$, such that for any finite subset $A$ of positive real
numbers with $|AA|\leq M|A|$, $|kA|\geq
\frac{C_k}{M^{D_k}}\cdot|A|^{\log_42k}.$
