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 Main {
    public static void main(String [] args){
        Scanner cin = new Scanner(System.in);
        double a,b,c,d;
        a=cin.nextDouble();
        b=cin.nextDouble();
        c=cin.nextDouble();
        d=cin.nextDouble();
        double u=(1-a/b)*(1-c/d);
        u=1/(1-u);
        System.out.printf("%.12f",u*(a/b));
    }
}