Fleecing the Raffle

A raffle gives out $p$ prizes. To enter, you write your name on a slip of paper and drop it into the raffle box. The winners are decided by drawing $p$ slips from the box. A drawn slip is not put back, so one person wins at most one prize.

Putting your name in more than once breaks the rules. The organizers do not check the names in the box, so you are caught only if your name is drawn for two or more prizes. Extra slips can therefore raise your chance of a prize.

Other people have put $n$ slips into the box. You add $k$ slips carrying your own name ($k \ge 1$), so the box holds $n + k$ slips and $p$ of them are drawn uniformly at random. Choose $k$ so that the probability that your name is drawn exactly once is as large as possible.

The first line contains two integers $n$ and $p$ separated by a space ($2 \le p \le n \le 10^6$). $n$ is the number of slips in the box other than yours, and $p$ is the number of prizes given away.

Print the largest possible probability of winning a prize on one line, rounded to exactly nine digits after the decimal point. Pad with zeros when digits are missing. For example, a probability of $0.6$ is printed as 0.600000000.