Étale extension of local fields

Question

Let $L/K$ be a finite extension of a local field $K$. Let $\mathfrak{p}$ be the unique prime in $\mathcal{O}_K$. Say $\mathfrak{p}$ factors as $\mathfrak{p} \mathcal{O}_L = \mathfrak{q}_1^{e_1} \cdots \mathfrak{q}_n^{e_n}$. When is $\mathcal{O}_{L} / \mathcal{O}_K$ étale in terms of the ramification indices and inertial degrees of $\mathfrak{p}$?