Score : 300 points

Problem Statement

Let us define the beauty of a sequence (a_1,... ,a_n) as the number of pairs of two adjacent elements in it whose absolute differences are d. For example, when d=1, the beauty of the sequence (3, 2, 3, 10, 9) is 3.

There are a total of n^m sequences of length m where each element is an integer between 1 and n (inclusive). Find the beauty of each of these n^m sequences, and print the average of those values.

Constraints

0 \leq d < n \leq 10^9
2 \leq m \leq 10^9
All values in input are integers.

Input

Input is given from Standard Input in the following format:

n m d

Output

Print the average of the beauties of the sequences of length m where each element is an integer between 1 and n. The output will be judged correct if the absolute or relative error is at most 10^{-6}.

Sample Input 1

2 3 1

Sample Output 1

1.0000000000

The beauty of (1,1,1) is 0.
The beauty of (1,1,2) is 1.
The beauty of (1,2,1) is 2.
The beauty of (1,2,2) is 1.
The beauty of (2,1,1) is 1.
The beauty of (2,1,2) is 2.
The beauty of (2,2,1) is 1.
The beauty of (2,2,2) is 0.
The answer is the average of these values: (0+1+2+1+1+2+1+0)/8=1.

Sample Input 2

1000000000 180707 0

Sample Output 2

0.0001807060