abstract algebra - Power of an $r$-cycle is an $r$-cycle

I'm trying to prove that if $\alpha$ is an $r$-cycle in $S_n$ then $\alpha^k$ is an $r$-cycle if and only if $(k,r)=1$, but I'm having trouble proving that if $(k,r)=1$ then $\alpha^k$ is an $r$-cycle.

Can someone help me with that?