Two logicians:

Two perfect logicians, S and P, are told that integers
x and y have been chosen such that 1 < x < y and x+y <
100. S is given the value x+y and P is given the
value xy. They then have the following conversation.

P: I cannot determine the two numbers.
S: I knew that.
P: Now I can determine them.
S: So can I.

Given that the above statements are true, what are the
two numbers?

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