[Logic] and the product of

And said S A P: I chose two integers x, y such that 1 <x <y and x + y <= 100. While I will secretly tell their S and s = x + y, I will secretly tell their product P p = xy. They then carried out the following dialogue:

• P: "I do not know these numbers."
• S: "I know that you do not know these numbers."
• P: "Now I know these numbers."
• S: "Now I know these numbers."

x and y is the number?