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}.

Examples

Input

2 3 1


Output

1.0000000000


Input

1000000000 180707 0


Output

0.0001807060
import java.util.*;

public class Main {
    public static void main(String[] args) {
        final Scanner sc = new Scanner(System.in);

        final double n = (double)sc.nextInt();
        final double m = (double)sc.nextInt();
        final double d = (double)sc.nextInt();

        // n = 4, m = 2, d = 0
        // (1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)
        // d = 0 (1,1),(2,2),(3,3),(4,4)
        // d = 1 (1,2),(2,1),(2,3),(3,2),(3,4),(4,3)
        // d = 2 (1,3),(2,4),(3,1),(4,2)
        // d = 3 (1,4),(4,1)

        double cn, cm, ret;
        if (d == 0) {
            cn = n;
        } else {
            cn = 2 * (n - d);
        }
        cm = m - 1;

        ret = cm * cn / (n * n);
        System.out.println(ret);
    }
}