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