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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Main {
    public static void main(final String[] args) {
        final FastScanner scanner = new FastScanner(System.in);
        final double n = scanner.nextInt();
        final double m = scanner.nextInt();
        final double d = scanner.nextInt();

        final double nodes = d == 0 ? n : (n - d) * 2;

        System.out.println(nodes / (n * n) * (m - 1));
    }

    private static class FastScanner {
        private final BufferedReader reader;
        private StringTokenizer tokenizer;

        FastScanner(final InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

        String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
    }
}
    