Gunnar and his friends like games which involve rolling
dice. Gunnar has a huge collection of 6sided, 12sided and
20sided dice. All the games with dice started to bore him, so
he came up with a new game. He rolls an $s$sided die $n$ times and wins if at least
$k$ different numbers
appear in the $n$ throws.
An $s$sided die contains
$s$ distinct numbers
$1, \dots , s$ on its
sides.
Since this is a game only for one person, Gunnar and his
friends decided to make it more fun by letting other people bet
on a particular game. Before you bet on a particular game, you
would like to know how probable it is to throw at least
$k$ different numbers in
$n$ throws with an
$s$sided die. We assume
that all numbers have the same probability of being thrown in
each throw.
Input
The input consists of a single line with three integers
$n$, $s$, and $k$ ($1\le n\le 10\, 000, 1 \le k \le s \le
500$). $n$ is the
number of throws, $k$ the
number of different numbers that are needed to win and
$s$ is the number of sides
the die has.
Output
Output one line with the probability that a player throws at
least $k$ different
numbers within $n$ throws
with an $s$sided die.
Your answer should be within absolute or relative error at most
$10^{7}$.
Sample Input 1 
Sample Output 1 
3 3 2

0.888888889

Sample Input 2 
Sample Output 2 
3 3 3

0.222222222
