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.math.*;
import java.io.*;

public class Main
{
	public static void main(String[] args) throws IOException
	{
//		BufferedReader c = new BufferedReader(new InputStreamReader(System.in));
		Scanner s=new Scanner(System.in);
		int a=s.nextInt(),b=s.nextInt(),c=s.nextInt(),d=s.nextInt();
		double p=(double)a/b,q=(double)c/d;
		double ans=p*(1/(1-(1-p)*(1-q)));
		System.out.format("%.9f%n",ans);
	}
}

//must declare new classes here