Professor Lazy, Ph.D.
Professors are very motivated when they have to travel abroad for a conference (of course, if fees are paid by the university), but they don’t have the same attitude when the moment to grade exams arrives.
Professor Lazy, Ph.D., has a particular way to grade exams (and very unfair, by the way). He puts all his exams in a box and then starts getting them out one by one in a totally random fashion. He assigns grade α to the first exam that he gets out of the box, and grade β to the second exam that he gets out of the box. From that point on, he assigns a grade to each of the exams based on the grades of the previous two exams. What he does is that he takes the grade of the immediately previous exam, adds 1 and divides by the grade of the exam before the previous one.
For example, let’s imagine that α = 2 and β = 3. This is what happens:
· The first exam gets α = 2.
· The second exam gets β = 3.
· The previous two grades are α and β, so the third exam gets = = 2.
· The previous two grades are β and , so the fourth exam gets = = 1.
· The procedure continues until he’s done with all exams.
More formally, we can define the grade Qn of the nth exam with a recurrence like this:
Even this simple procedure is a lot of work for Professor Lazy, Ph.D., so he asks you to write a program to do it for him. He wants to spend all day long drinking coffee in the cafeteria with other professors. Given α, β and n find the value of Qn.
Note that the grades do not necessarily lie inside a fixed range. They are just arbitrary integers.
The last line of the input contains three zeros and should not be processed.
1 1 0 1 2 1 5 9 2 2 3 3 7 4 4 0 0 0
1 2 2 1 2