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 BArcher {
	public static void main(String[] args) {
		Scanner k = new Scanner(System.in);
		double a,b,c,d,r1,r2;
		a=k.nextDouble();
		b=k.nextDouble();
		c=k.nextDouble();
		d=k.nextDouble();
		
		r1=a/b;
		r2=c/d;
		
		r1/=(1-((1-r1)*(1-r2)));
		System.out.println(r1);
		
	}
}