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.io.*;

public class Main {
    public static final double EPS = (int)1E-9;
    public static double prob(int a, int b, int c, int d) {
        double psr = (double)a / b;
        double pz  = (double)c / d;
        double qsr = 1 - psr;
        double qz  = 1 - pz;
    
        double curr = 1.0;
        double goal = 0.0;
        double tgoal = 0.0;
    
        do {
            tgoal = goal;
            goal = goal + curr * psr;
            curr = curr * qsr * qz;
        } while (Math.abs(tgoal - goal) > EPS);
        return goal;
    }
    
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int a = scan.nextInt();
        int b = scan.nextInt();
        int c = scan.nextInt();
        int d = scan.nextInt();
        System.out.println(prob(a, b, c, d));
    }
}