Problem Statement

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.

Input

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

Output

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

Constraints

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

Sample Input 1

3 2 2

Sample Output 1

0.468750000000000

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

Sample Input 2

200000 200000 200000

Sample Output 2

0.999986408692793

见题面 Input 部分

见题面 Output 部分