You will play a game against a dealer. The game uses a $D$-sided die (dice) that shows an integer from $1$ to $D$ with equal probability, and two variables $x$ and $y$ initialized to $0$. The game proceeds as follows:

-   You may perform the following operation any number of times: roll the die and add the result to $x$. You can choose whether to continue rolling or not after each roll.
    
-   Then, the dealer will repeat the following operation as long as $y < L$: roll the die and add the result to $y$.
    
-   If $x > N$, you lose. Otherwise, you win if $y > N$ or $x > y$ and lose if neither is satisfied.
    
Determine the probability of your winning when you act in a way that maximizes the probability of winning.

The input is given from Standard Input in the following format:

```
$N$ $L$ $D$
```

Print the answer. Your output will be considered correct if its absolute or relative error from the true value is at most $10^{-6}$.

-   All inputs are integers.
-   $1 \leq L \leq N \leq 2 \times 10^5$
-   $1 \leq D \leq N$

0.468750000000000

It can be proved that the optimal strategy is to continue rolling as long as x is not greater than 2.