A third party picks two integers, X and Y, each from the interval 2 to 99, and tells Mr. Sam the sum of the two integers, and Mr. Paul the product of the two. Sam and Paul do not know the values given to the other. Paul tells Sam, “I do not know the two integers.” Sam tells Paul, “I know you didn’t. Neither do I.” Paul replies, “Oh, now I know the integers.” Sam replies back, “Now I know too.”

Given that both of them are telling the truth, what are the two integers.

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