Expectation of a product from a product pmf

Let $X$ and $Y$ be two positive integer valued random variables with the joint probability mass function

$$P(X=m,Y=n)=\begin{cases}g(m)h(n), & m,n\ge1,\ 0, & \text{otherwise,}\end{cases}$$

where $g(m)=\left(\frac12\right)^{m-1}$, $m\ge1$ and $h(n)=\left(\frac13\right)^n$, $n\ge1$. Then $E(XY)$ equals ____________