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.BufferedReader;
import java.io.BufferedWriter;
import java.io.File;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner sc = null;
        PrintWriter pr = null;
        
        try {
            pr=new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
            sc = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
            //sc = new Scanner(new File("input.txt"));
        } catch (Exception e) {
            e.printStackTrace();
        }
        
        
        int a = sc.nextInt();
        int b = sc.nextInt();
        int c = sc.nextInt();
        int d = sc.nextInt();
        
        
        double x = 1.0 * a / b;
        double y = 1.0 * c / d;
        double res = x/(1-(1-x)*(1-y));
        pr.println(res);
        
        pr.close();
        sc.close();
    }
}