Mr. B and Mr. M like to play with balls. They have many balls colored in blue and red. Firstly, Mr. B randomly picks up balls out of them and put them into a bag. Mr. M knows that there are possible situations in which the number of red balls is ranged from to , and we assume the possibilities of the situations are the same. But Mr. M does not know which situation occurs. Secondly, Mr. M picks up balls out of the bag and examines them.
There are red balls and blue balls. The question is: if he picks up one more ball out of the bag, what is the possibility that this ball is red?
输入格式
Each test case contains only one line with three integers and .
输出格式
For each test case, display a single line containing the case number and the possibility of the next ball Mr. M picks out is red. The number should be rounded to four decimal places.
样例
样例输入 #1
3 0 0
4 2 1
样例输出 #1
Case 1: 0.5000
Case 2: 0.5000
数据范围与提示
对于 的数据，，，。
[Explanation]
For example as the sample test one, there are three balls in the bag. The possibilities of the four possible situations are all . If there are no red balls in the bag, the possibility of the next ball are red is . If there is one red ball in the bag, the possibility is . If there are two red balls, the possibility is . Finally if all balls are red, the possibility is . So the answer is .
