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 b312
{
public static void main(String args[])throws IOException
    {
        double a,b,c,d,m,n;
        InputStreamReader read=new InputStreamReader(System.in);
        BufferedReader in=new BufferedReader(read);
        //System.out.println("Enter a ,b,c,d");
        String str=in.readLine();
        StringTokenizer aa=new StringTokenizer(str);
        a=Double.parseDouble(aa.nextToken());
        b=Double.parseDouble(aa.nextToken());
        c=Double.parseDouble(aa.nextToken());
        d=Double.parseDouble(aa.nextToken());
        m=1.0-a/b;
        n=1.0-c/d;
        System.out.println((a/b)/(1.0-m*n));
    }
}