Yet another puzzle

We pick two numbers a and b, so that a>=b and both numbers are within
the range [2,99]. We give Mr.P the product a*b and give Mr.S the sum
a+b.

The following dialog takes place:

Mr.P: I don't know the numbers
Mr.S: I knew you didn't know. I don't know either.
Mr.P: Now I know the numbers
Mr.S: Now I know them too

Can we find the numbers a and b?

I must admit ... my feeble mind couldn't comprehend that this puzzle even had solution when I first saw it. However, now I know that it does, and am still trying to work it out. If you are a bit impatient - Google around, you'll find the answer.