Yesterday, I read in detail about the giant baby steps algorithm.
I had heard about him before, but did not delve into the gist of it.
This algorithm is very similar to the one I use.
So you have use this algorithm which is in O(sqrt(n)) for both memory and time where n is the size of the range.
Staring with an offset does not prevent to use this algorithm.
That means that the key rate (or group operation) you announced is wrong.
Do not waste time in solving the above problem, solving it will just prove that you have correctly implemented this known algorithm.