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 java.io.*;

public class second 
{
	public static void main(String args[])
	{
		int a,b,c,d;
		Scanner sc = new Scanner(System.in);
		a=sc.nextInt();
		b=sc.nextInt();
		c=sc.nextInt();
		d=sc.nextInt();
		double a1 =(double)a/b;
		double c1= (double)c/d;
		double r = (1.0-a1)*(1.0-c1);
		double result = a1/(1-r);
		System.out.println(result);
	}
}