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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;
import java.util.*;
import java.io.*;
import java.lang.*; 
public class Solution {
    public static void main(String[] args)throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter wr = new BufferedWriter(new OutputStreamWriter(System.out));
       
       String str[] = br.readLine().split(" ");
        double a = Double.parseDouble(str[0]);
        double b  = Double.parseDouble(str[1]);
          double c = Double.parseDouble(str[2]);
       double d = Double.parseDouble(str[3]);
        
      
           double num = (1.0*a/b)/(1-((1-(1.0*a/b))*(1-(1.0*(c/d)))));
            System.out.format("%.12f",num);
        
}
}