You are given a pizza (perfect circle) that has been cut into $m\cdot n$ equal pieces and you want to have exactly one topping on each slice.

Let $f(m,n)$ denote the number of ways you can have toppings on the pizza with $m$ different toppings ($m\ge 2$), using each topping on exactly $n$ slices ($n\ge 1$).
Reflections are considered distinct, rotations are not.

Thus, for instance, $f(2,1)=1$, $f(2,2)=f(3,1)=2$ and $f(3,2)=16$.
$f(3,2)$ is shown below:

Find the sum of all $f(m,n)$ such that $f(m,n)\le {10}^{15}$.