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。

49愛的鼓勵 6訂閱站台

Consider the following scenario:

You are a University Student; all of your friends consider you courageous, most of the girls find you handsome, you are quite a good student, recently your team has won a regional contest of ACM ICPC and so your confidence is very high. In a party you find someone nice and ask her to dance but she seems smarter than (as always is the case) you. She tells you, “There are M gentle men and W ladies in this party except us. You have C candies in your hand and you distribute them randomly among all these guests (M men and W ladies), of course if possible. Now you collect all the candies from all the gentlemen and this number of candies is CC. If you can evenly distribute these (CC) candies equally between two groups (These two groups are two arbitrary groups) I will dance with you.”  

Now tell me what is the probability of her dancing with you?

Input

The input file contains several lines of input. Each line contains three non-negative integers M (M<=1000), W (W<=1000) and C (C<=100). The meanings of the symbols are explained before. The input is terminated by a line where M=0 and W=0. You need not process this input.

Output

For each line of input, you should produce one line of output, which is a floating-point number. This output is the probability of her dancing with you. The number contains seven digits after the decimal point. An error less than 2E-7 or 2* 10^(-7) will be overlooked.

Sample Input:

Sample Output: