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.InputStreamReader;
import java.io.BufferedReader;
public class cdf185b 
{
	public static void main(String args[])throws Exception
	{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		String s=br.readLine();
		String ss[]=s.split(" ");
		double a=Integer.parseInt(ss[0]);
		double b=Integer.parseInt(ss[1]);
		double c=Integer.parseInt(ss[2]);
		double d=Integer.parseInt(ss[3]);
		double temp=(1-(a/b))*(1-(c/d));
		double ans=a/b*(1/(1-temp));
		System.out.println(ans);
	}	
}