Not Quasicoherent Sheaf on $\mathbb{P}_k ^1$

Question

Let $\mathbb{P}_k ^1$ the projective line as scheme over a field $k$ (therefore two glued copies of $\mathbb{A}_k ^1$. I'm looking for an example of a sheaf on $\mathbb{P}_k ^1$ which isn't quasicoherent.