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:
//Created by Aminul on 4/10/2020.

import java.io.*;
import java.util.*;

import static java.lang.Math.*;

public class B {
    public static void main(String[] args) throws Exception {
        Scanner in = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        double a = in.nextInt(), b = in.nextInt();
        double c = in.nextInt(), d = in.nextInt();
        double p = 0;
        for (int i = 1; i < 1e5; i++) {
            p += pow(1.0 - (a / b), i - 1) * (a / b) * pow(1.0 - (c / d), i - 1);
        }
        pw.println(p);
        pw.close();
    }

    static void debug(Object... obj) {
        System.err.println(Arrays.deepToString(obj));
    }
}