I tried to solve with some float precisions but it was always WA. Then it was written using only integer calculations and AC.

I got AC using doubles

But integer solution really nice ;)

I think that integer method is nice
because it mathematically easy proved
Float method has only timus-Ac verification and
there for less nice.
I tried to find regorious analysis of some
float algo based on computer float system theory but it is rather difficult.

I totally agree - very interesting problem with integer solution.