elementary number theory - Proving that $p^{alpha + beta + 1} mid {n choose k} p^{kalpha}$ when $p^beta mid n$.

Let $n,\alpha\in\mathbb{N},\beta\in\mathbb{N}_0$, and let $p$ be odd prime number s.t. $p^\beta|n$.

How do we prove that $p^{\alpha+\beta+1}|{n\choose k}p^{k\alpha}$ for every $k\in\{1,2,\ldots,n-1\}$?