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:
/*
 * To change this template, choose Tools | Templates
 * and open the template in the editor.
 */


import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

/**
 *
 * @author Prakhar Sharma
 */
public class codeforces1 {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) throws IOException {
        
          BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
      String firstLine = br.readLine();  // 1st line contains only # of vertices
      StringTokenizer token = new StringTokenizer(firstLine);
      double a=Float.parseFloat(token.nextToken());
      double b=Float.parseFloat(token.nextToken());
      double c=Float.parseFloat(token.nextToken());
      double d=Float.parseFloat(token.nextToken());
      
     // System.out.println(a +" "+b+" "+c+" "+d);
      double ans=(a*d)/(a*d+b*c-a*c);
      System.out.println(ans);
    }
}