Pareto III random variate

Hello,
I need to generate a random variate distributed according a Pareto III,
essentially a pareto with an exponential dumping. The distribution is

F(x) = 1-(x/s+1)^{-a}*exp(-b*x/s) x \in [0,+\inty)

does someone have some idea on how to do it (apart generating an
uniform in [0,1) and numerically inverting F) ?

Many thaks,

Giulio.
.