Problem: SmallR is an archer. SmallR is taking a match of archer with Zanoes. They try to shoot in the target in turns, and SmallR shoots first. The probability of shooting the target each time is <image> for SmallR while <image> for Zanoes. The one who shoots in the target first should be the winner.

Output the probability that SmallR will win the match.

Input

A single line contains four integers <image>.

Output

Print a single real number, the probability that SmallR will win the match.

The answer will be considered correct if the absolute or relative error doesn't exceed 10 - 6.

Examples

Input

1 2 1 2


Output

0.666666666667

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.util.Scanner;

/**
 * Created with IntelliJ IDEA.
 * User: Alexander Shchegolev
 * Date: 26.05.13
 * Time: 17:49
 * To change this template use File | Settings | File Templates.
 */
public class Two {
    public static void main(String[] args) throws IOException {
        Scanner scanner = new Scanner(System.in);
        int a = scanner.nextInt();
        int b = scanner.nextInt();
        int c = scanner.nextInt();
        int d = scanner.nextInt();
        double p = (double) a / (double) b;
        double q = (double) c / (double) d;
        double P = p * (1 / (1 - (1 - p) * (1 - q)));
        System.out.printf("%12.11f", P);
    }

}