Dice Betting

Gunnar and his friends like games that involve rolling dice. Gunnar owns a huge collection of 6-sided, 12-sided and 20-sided dice. Every dice game he knew had become boring, so he invented a new one. He rolls an $s$-sided die $n$ times and wins if at least $k$ different numbers appear in those $n$ throws. An $s$-sided die carries the numbers $1$ to $s$ on its sides, one distinct number per side.

The game has a single player, so Gunnar and his friends made it more fun by letting other people bet on a round. Before you bet, you want to know how probable it is to throw at least $k$ different numbers in $n$ throws with an $s$-sided die. Every number is equally likely on each throw.

The only line contains three integers $n$, $s$ and $k$ in this order ($1 \le n \le 10\,000$, $1 \le k \le s \le 500$). $n$ is the number of throws, $s$ is the number of sides of the die, and $k$ is the number of different numbers needed to win.

Print one line with the probability that at least $k$ different numbers appear in $n$ throws of an $s$-sided die. Round the value to nine digits after the decimal point and pad with zeros so that exactly nine digits follow the decimal point. A probability of $1$ prints as 1.000000000 and a probability of $0$ prints as 0.000000000.