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.io.*;
import java.util.*;

public class archer {
	public static int a, b, c, d;
	public static double x, y;
	
    public static void main(String[] args) throws Exception {
    	Scanner in=new Scanner(System.in);
    	a=in.nextInt();
    	b=in.nextInt();
    	c=in.nextInt();
    	d=in.nextInt();
    	x=(double)a/b;
    	y=(double)c/d;
    	System.out.println((x)/(1-(1-x)*(1-y)));
    }
}