Let $U = \left\{ (x, y) \in \mathbb{R}^2 \mid 1 < x^2 + y^2 < 4 \right\}$. Let $p, q \in U$. Show that there is a continuous map $\gamma : [0,1] \longrightarrow U$ such that $\gamma(0) = p$ and $\gamma(1) = q$ and such that $\gamma$ is differentiable on $(0,1)$.