How to efficiently generate random number from COM-POISSON distribution via mean parametrization in R?

I know that mpcmp::dcomp() generates random numbers from COM-Poisson distribution. However, they fail to generate such data if mean is large.

The following example doesn't compute, or take to much time:

mpcmp::rcomp(1, mu = 500, nu = 1)

So. How to generate a COM-Poisson data with large mean efficiently?

Thanks!