Hello everyone!
Today I was solving a problem and I reduced it to finding a maximum of a function. So in short what I need is the following:
, where M, a, b ≤ 109.
It's obvious that 
iff 
, but I cannot find an easy way to get the maximum if 
. I will appreciate any help on the problem.
PS: a, b and M are given as queries so I need an algorithm to answer up to 105 queries.
UPDATE: It's actually pretty simple. 
actually has values of form 
. Then it's obvious that the solution will be 
.
Have you thought about the case where a = 0? What values can you get for f then? What's the max then? Is it much harder when a ≠ 0?
Thanks a lot. I figured it out.