This only works if you read all pages one by one. But if you have 100+ pages document and want to jumt to page 63 you gona have a bad time.
With this one, I know the last page is around 50 in the normal order. So I will just invert the stack and scan linearly for 63 from the bottom.
Or alternatively: The first step of your binary search is to look at the page number on the flip side of page 1 and determine to flip the stack or not.