Finding a map which induces isomorphism in Homology

Question

Let $X$ be a topological space such that $H_i(X)=0$ for all $1<i<n$. Let $H_n(X)=\pi$. Now I want to find a map $f:X \to K(\pi,n)$ such that $H_n(f)$ and $\pi_n(f)$ are isomorphisms. Can anyone give some hints as to how one gets this map. Thank you.