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.awt.Point;
import java.util.ArrayDeque;
import java.util.Scanner;
import java.util.*;
import java.util.Arrays;
import java.util.ArrayList;
import java.util.Set;
import java.util.HashSet;
import java.util.Collection;


 
public class Main{
	
        static final Scanner sc=new Scanner(System.in);
        static double n=sc.nextInt();
        static double m=sc.nextInt();
        static double d=sc.nextInt();
        
        
        
        
        
        public static void main(String[]args){
                double x=2/n;
                double y=2*d;
                double z=n*n;
                double yy=y/z;
                if(d!=0){
                System.out.println((x-yy)*(m-1));}
                else{
                        System.out.println((x-yy)*(m-1)/2);

                }

                
                
                

        }
        
        
        

		
	
}
