Divisibility of a binomial coefficient by a prime

Let $q=p^r,$ where $p\in\mathbb{P}$ is a prime and $r\in\mathbb{N}\setminus\{0\}$ is a natural number (non-zero). How to prove that for each $i\in\{1,2,\ldots,q-1\}$ the binomial coefficient $\binom{q}{i}$ is divisible by $p$?

I find it easy to show that $p|\binom{p}{i},$ but here it's more complicated :/