Recognition of simple groups $B_p(3)$ by the set of element orders

Let $G$ be a finite group and let $\omega(G)$ be the set of its element orders. We prove that if $\omega(G)=\omega(B_p(3))$ where $p$ is an odd prime, then $G\cong B_3(3)$ or $D_4(3)$ for $p=3$ and $G\cong B_p(3)$ for $p>3$.