In the parallelogram $ABCD$ of the figure, $\overrightarrow{AB} = \vec p$ and $\overrightarrow{AD} = \vec q$. Which vector is $\overrightarrow{BD}$?

Fig. 1: A parallelogram ABCD with A at the bottom left, B at the bottom right, C at the top right and D at the top left. A blue arrow p runs from A to B along the bottom side, and a green arrow q runs from A to D along the left side. A red dashed line joins B to D.