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.Scanner;

public class Main {
    Scanner cin;

    public static void main(String[] args) throws Exception {
        Main mn = new Main();
        mn.cin = new Scanner(System.in);
        mn.solve();
    }

    private void solve() throws Exception {
        int a = cin.nextInt();
        int b = cin.nextInt();
        int c = cin.nextInt();
        int d = cin.nextInt();
        double numerator = a * d;
        double denominator = (b * d - (b - a) * (d - c));
        double answer = numerator / denominator;
        System.out.println(answer);
    }
}