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.*;
import java.math.BigDecimal;

public class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    double n = sc.nextDouble();
    double m = sc.nextDouble();
    double d = sc.nextDouble();
    BigDecimal bd1 = new BigDecimal(2 * (n - d));
    if(d == 0) bd1 = new BigDecimal(n - d);
    BigDecimal bd2 = new BigDecimal(m - 1);
    BigDecimal bd3 = new BigDecimal(n * n);
    BigDecimal bd4 = bd1.multiply(bd2);
    BigDecimal result = bd4.divide(bd3, 10, BigDecimal.ROUND_HALF_UP);
    System.out.println(result);
  }
}