## sequence of distinct points, cluster values

Let $\{ z_k \}$ be a sequence of distinct points in a domain $D$ that accumulates on $\partial D$, and let $E$ be a nonempty closed subset of the extended complex plane $\overline{\mathbb{C}}$. Show that there is an analytic function $f(z)$ on $D$ such that $E$ is the set of cluster values of $f(z)$ along the sequence $\{ z_k \}$.

I am not sure how to prove this. I would appreciate a few hints or suggestions. In this section we have covered Runge's Theorem. However, I am still not sure how to prove this. I don't see how to show the existence of such an analytic function $f(z)$. Thanks in advance.