A Famous Game#3590
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 puts them into a bag. Mr. M knows that there are N+1 possible situations in which the number of red balls ranges from to , and we assume the possibilities of the N+1 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 P-Q blue balls. The question is: if he picks up one more ball out of the bag, what is the probability that this ball is red?
Each test case contains only one line with three integers , and (2 \le N \le 100000, 0 \le P \le N-1, 0 \le Q \le P).
For each test case, display a single line containing the probability that the next ball Mr. M picks out is red. The number should be rounded to four decimal places.
Example 1
For example as in the sample test, there are three balls in the bag. The probabilities of the four possible situations are all . If there are no red balls in the bag, the probability that the next ball is red is . If there is one red ball in the bag, the probability is . If there are two red balls, the probability is . Finally if all balls are red, the probability is . So the answer is 0 \cdot (1/4)+(1/3) \cdot (1/4)+(2/3) \cdot (1/4)+1 \cdot (1/4)=0.5.