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.*;
import static java.lang.Math.*;

public class B312 {
	private Scanner input = new Scanner(System.in);
	public static void main(String[] args) {
		B312 okok = new B312();
		okok.solve();
	}
	public void solve() {
		double a,b;
		double x,xx,y,yy;
		x=input.nextDouble();
		xx=input.nextDouble();
		y=input.nextDouble();
		yy=input.nextDouble();
		a=x/xx;
		b=y/yy;
		System.out.println(a/(1-(1-a)*(1-b)));
	}
}