The teacher tells Summo and Prodo: "I have picked three positive integers $x\le y\le z$. I have whispered the sum $S=x+y+z$ into Summo's ear, and I have whispered the product $P=xyz$ into Prodo's ear." Now the following conversation takes place.
Summo: "I do not know $x,y,z$. But if I knew that your number $P$ is greater than my number $S$, then I would be able to determine $x,y,z$."
Prodo: "Aha! Actually my number $P$ is less than your number $S$. And I am able to determine $x,y,z$."
Question: What are these numbers $x,y,z$?