cuRAND restart question

I am running a long time simulation, and need to call cuRAND many times (using a fixed random number seed in the beginning). For some reason like power failure, the simulation stops in the middle. But I do not want to re-run the code from the beginning, I need to save some information in order to continue cuRAND generation. What should I save? offset or some other variables? Because the random number sequence should be the same as no power failure happens. Does anyone has this experience?