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.Scanner;

public class Main {

    static Scanner scanner;

    public static void main(String[] args) {
        scanner = new Scanner(System.in);

        double n=gl();
        double m=gl();
        double d=gl();
        double ans =0;
        if (d==0) {
        	ans = (m-1)/n;
        } else {
        	ans = (m-1) * 2 * (n-d)/ n/n;
        }
        System.out.println(ans);
    }


    // 文字列として入力を取得
    public static String gs() {
         return scanner.next();
    }

    // intとして入力を取得
    public static int gi() {
         return Integer.parseInt(scanner.next());
    }

    // longとして入力を取得
    public static long gl() {
         return Long.parseLong(scanner.next());
    }

    // doubleとして入力を取得
    public static double gd() {
         return Double.parseDouble(scanner.next());
    }
}