The Raffle (Raffling for the Goose) by William
Sidney Mount, public domain
A tremendously exciting raffle is being held, with some
tremendously exciting prizes being given out. All you have to
do to have a chance of being a winner is to put a piece of
paper with your name on it in the raffle box. The lucky winners
of the
$p$ prizes are
decided by drawing
$p$
names from the box. When a piece of paper with a name has been
drawn it is not put back into the box – each person can win at
most one prize.
Naturally, it is against the raffle rules to put your name
in the box more than once. However, it is only cheating if you
are actually caught, and since not even the raffle organizers
want to spend time checking all the names in the box, the only
way you can get caught is if your name ends up being drawn for
more than one of the prizes. This means that cheating and
placing your name more than once can sometimes increase your
chances of winning a prize.
You know the number of names in the raffle box placed by
other people, and the number of prizes that will be given out.
By carefully choosing how many times to add your own name to
the box, how large can you make your chances of winning a prize
(i.e., the probability that your name is drawn exactly
once)?
Input
The input consists of a single line containing two integers
$n$ and $p$ ($2
\le p \le n \le 10^6$), where $n$ is the number of names in the
raffle box excluding yours, and $p$ is the number of prizes that will
be given away.
Output
Output a single line containing the maximum possible
probability of winning a prize, accurate up to an absolute
error of $10^{6}$.
Sample Input 1 
Sample Output 1 
3 2

0.6

Sample Input 2 
Sample Output 2 
23 5

0.45049857550
