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 Mentors {
    public static void main(String x[])
    {
        Scanner sc=new Scanner(System.in);
        double a=sc.nextDouble(),b=sc.nextDouble(),c=sc.nextDouble(),d=sc.nextDouble();
        double p1=(a/b);
        double p2=(double)(c/d);
        double p3=(1.0-(1-p1)*(1-p2));
        double s=(double)(p1/p3);
        System.out.println((double)s);
    }
            
}