Hamiltonian bipartite graphs

Question

Let $G$ be a bipartite graph with $n$ vertices and independent sets $U$ and $V$ such that $\vert U\vert=\vert V\vert=k=\frac{n}{2}>2$.

I want to show that if $d(v)>\frac{k}{2}$ for every vertex $v$ of $G$, then $G$ is Hamiltonian.