Chef and Bulb Invention

Chef is trying to invent the light bulb that can run at room temperature without electricity. So he has $N$ gases numbered from $0$ to $N - 1$ that he can use and he doesn't know which one of the $N$ gases will work but we do know it. Now Chef has worked on multiple search algorithms to optimize search. For this project, he uses a modulo-based search algorithm that he invented himself. So first h