Strong-Willed Victory#2155
Yuri loves football. He is very happy when his favorite team wins. He is even happier when it is a come-from-behind victory. A come-from-behind victory means the team wins, but was losing at least at one moment during the match.
Yuri learned that his favorite team won their last match. However, he does not know how the game unfolded, and now he is interested in the probability that it was a come-from-behind victory. Assume that every scenario for the course of the match is equally likely. A scenario is defined by the order in which both teams score their goals.
The input consists of two integers: — the number of goals Yuri's favorite team scored, and — the number of goals scored by the rival team, where 0 \leq b < a \leq 1\,000\,000.
Print the probability that the last match of Yuri's favorite team was a come-from-behind victory, with six digits after the decimal point.
One of the three possible match scenarios is a come-from-behind victory: when the rival team scores the first goal. In the other two scenarios, Yuri's favorite team never loses at any moment.
Example 1