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 {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc = new Scanner(System.in);
		
		int n = sc.nextInt();
		int m = sc.nextInt();
		int d = sc.nextInt();
		
		//確率の計算
		//1パターンずつしかないもの
		double x1 = 0;
		if(n > d){
			x1 = 1.0/n/n * d * 2;
		}
		
//		System.out.println(x1);
		
		//2パターンありえるもの
		double x2 = 0;
		if(n > 2*d){
			x2 = 1.0/n/n * (n - 2*d);
		}
		if(d != 0){
			x2 *= 2.0;
		}
//		System.out.println(x2);
		
		double x3 = x1 + x2;
		
		System.out.printf("%.10f\n",x3*(m - 1));
	}

}
