Morris' Blog 我在摸索我存在的意義、生命的意義、內涵及價值。 沒有真正神手般的厲害，套用模式是大部分的情況。 沒那麼厲害的我存在的意義為何，襯托出神的存在？ 有時候不能怪別人不給我機會，我已經開始省思， 為什麼我沒有給別人機會的原因，而是全要靠別人。 有時候我認為我與眾不同，那是因為我做不到很多人能辦到的事情。 我聽不到、玩不起來、說得不夠明瞭、理解得不夠多， 我缺少的語文能力，就是一切一切無能的判定。 為此，我不曉得能做些對別人有幫助的事情。 我知道我自己是個不服輸的性格，但現在我不得不認輸。 我沒有能力，因此我必須認輸。 我到底來這世界作什麼？處處充滿不確定性， 而我總是無法出類拔萃，想當個一般人似乎也回不了頭了。 越強大的挑戰需要越強力的支持，而我的支持是什麼？ 最近嘗試與人談話，但都是失敗的結局，沒人能接受， 不需要言語，不需要溝通，一切所想都表達不出來。

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Problem D. 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 Q_n of the nth exam with a recurrence like this:

Qn =

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 Q_n.

Note that the grades do not necessarily lie inside a fixed range. They are just arbitrary integers.

Input

The input contains several test cases (at most 1000). Each test case is described by three integer numbers α, β and n on a single line (1 ≤ α, β ≤ 10⁹ and 0 ≤ n ≤ 10¹⁵).

The last line of the input contains three zeros and should not be processed.

Output

For each test case, write the value of Q_n in a single line. The input will be such that the value of Q_n is always an integer. Furthermore, Q_i will never be zero for 0 ≤ i ≤ n (in other words, division by zero will never arise when evaluating the recurrence).

Sample input and output