P is told the product of two integers chosen from [2, 99] and S is told the sum. The following dialogue ensues:
(1) P says, "I do not know the two integers."
(2) S replies, "I knew that already."
(3) P exclaims, "Ah! I now know the two numbers.",
(4) S smugly replies, "Now I know them too."
What are the two numbers?