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 void main(String args[])
{
	Scanner sc=new Scanner(System.in);
	int a=sc.nextInt();
	int b=sc.nextInt();
	int c=sc.nextInt();
	int d=sc.nextInt();
	double s=((double)a)/b;
	double t=((double)(b-a))/b;
	double f=((double)(d-c))/d;
	double g=t*f;
	double h=1-g;
	double r=s/h;
	System.out.println(r);
}
}