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 {
    static int modP = 1000000007;
    static long inf  = 1 << 61;
    static int[] x4 = {-1, 0, 0, 1};
    static int[] y4 = {0, -1, 1, 0};

    static double n, m, d, s, t;
    static int[] U, V, A, B;

    public static void main(String[] args) {
        input();
        solve();
    }

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

    static void input() {
        Scanner in = new Scanner(System.in);
        n = in.nextDouble();
        m = in.nextDouble();
        d = in.nextDouble();
    }

    static void print(String s) {
        System.out.println(s);
    }

    static void print(char c) {
        System.out.println(c);
    }

    static void print(int i) {
        System.out.println(i);
    }

    static void print(long i) {
        System.out.println(i);
    }

    static void print(float i) {
        System.out.println(i);
    }

    static void printArray2D(int[][] array, char del) {
        int r = array.length;
        int c = array[0].length;
        for(int i = 0; i < r; i++) {
            for(int j = 0; j < c; j++) {
                System.out.format("%3d", array[i][j]);
                if(j != c-1) System.out.print(del);
                else System.out.print('\n');
            }
        }
    }
}