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.PrintWriter;
import java.util.Scanner;

public class Task
{
    static PrintWriter out;
    static Scanner in;
    
    static final int MAX = 100000;
    
    public void solve() {
        int a = in.nextInt(), b = in.nextInt(), c = in.nextInt(), d = in.nextInt();
        double ans = 0, prob = 1.;
        for (int i = 0 ;i < MAX; ++i) {
            ans += prob * a / b;
            prob *= (1. - (double) a / b);
            prob *= (1. - (double) c / d);
        }
        out.println(ans);
    }
    
    public static void main(String[] args) {
        out = new PrintWriter(System.out, true);
        out.flush();
        in = new Scanner(System.in);
        new Task().solve();
    }
}