Zero dimensional subscheme and section of a sheaf on $\mathbb P^2$

Let $E$ be a vector bundle of rank $2$ on $\mathbb P^2$ and $Z$ be zero dimensional subscheme of length $k$ supported on a point $p \in \mathbb P^2$. What is the number $h^0(E(m) \times \mathscr O_Z)$ for an integer $m$?

My intuition is that it should be $2k$. But it seems in some literature it is suggested to be $k(k+1)$.

Any comments, suggestions is welcome.