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.util.Scanner;

public class Archer {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        double a = sc.nextInt();
        double b = sc.nextInt();
        double c = sc.nextInt();
        double d = sc.nextInt();
        double r = (1-c/d)*(1-a/b);
        System.out.println((a/b)/(1-r));
    }
}