Rahul Mehta Gandhinagar LsCandidate

Math puzzle : (NOT RELATED TO POLITICS)

There are 3 persons in room
.
Host, two players S and P.
.
Host decides two nunbers 1 < x <= y < 100 i.e. x and y are between 1 and 100, but not 1 or 100 and can be equal
.
Then host gives product x * y to P
.
And then host gives sum = x + y to S
.
P says -- I cant decide x , y
.
S says -- I already knew that you wont be able decide x or y. Nor can I decide x or y
.
P says --- ah !! now I know x and y
.
S says -- aha, now I also know x and y
.
---
.
What is value of x and y
.
Hint : write code
.
Also, note that ONLY one pair of (x , y ) exists in 2 <= x <= y <= 100 which create such communication. For other x y combination, this communiation wont come

Mathematics: An Integral Part of Happiness: