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.*;
public class Archer {
public static void main(String[] args)
{
    Scanner s=new Scanner(System.in);
    double a=s.nextInt();
    double b=s.nextInt();
    double c=s.nextInt();
    double d=s.nextInt();
    
    double prob=(a/b)*(1/(1-(1-a/b)*(1-c/d)));
    System.out.println(prob);
    
}
}