I have chosen two different numbers greater than N but less than M. I tell their sum to Mr. S and their product to Ms. P. The following conversation ensues:

Mr. S: I cannot determine the two numbers.
Ms. P: I cannot determine the two numbers either.
Mr. S: I still cannot determine the two numbers.
Ms. P: Now I can determine the two numbers.
Mr. S: Now I can determine the two numbers also.

Find the greatest value of M for which this puzzle has a unique solution, for N=1, N=2 and N=3.