Puzzle n°9 (***) - The "Som" and the Product

Alyse and Babette are talking about their respective experience as aby and somali breeders.

Two of their friends arrive, Sabine and Pierre, who enjoy mathematics puzzles.
Alyse and Babette tell them that they have bred several kittens each, but less than 100, and that Alyse has bred more than Babette.
For the fun, they don't tell Sabine and Pierre the exact number of kittens that they have bred,
but they tell Sabine the sum of the the two numbers, and they tell Pierre their product.
The following conversation then takes place:

Pierre: "I don't know the number of kittens that each of you bred"
Sabine: "I knew you didn't know"
Pierre: "Ah ah... Now I know !"
Sabine: "And me too !"

What about you ? Do you know how many kittens Alyse and Babette have each raised ?

... I'm giving up ...