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 asd[])throws Exception
    {
        Scanner in=new Scanner(System.in);
        int a=in.nextInt();
        int b=in.nextInt();
        int c=in.nextInt();
        int d=in.nextInt();
      
        double f=((double)a/b)*(1.0/(1.0-((1.0-(1.0*a)/b)*(1.0-(1.0*c)/d))));
        System.out.println(f);
    }
}