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:
//package albert.codeforces.archer312b;

import java.util.Scanner;

public class Solution {
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        final double a = scan.nextDouble();
        final double b = scan.nextDouble();
        final double c = scan.nextDouble();
        final double d = scan.nextDouble();

        /*double a = 1;
        double b = 2;
        double c = 1;
        double d = 2;*/


        System.out.println(solve(a, b, c, d));
    }

    private static double solve(double a, double b, double c, double d) {
        double sWin = a / b;
        double sLoose = 1.0 - sWin;
        double zLoose = 1.0 - (c / d);
        double delta = 1e-9;
        double last = sWin;
        int t = 1;
        while (true) {
            double next = lost(t++, sLoose, zLoose) * sWin + last;
            if (Math.abs(next - last) < delta) {
                break;
            }
            last = next;
        }
        return last;
    }

    private static double lost(int t, double sLoose, double zLoose) {
        double ans = 1;
        while (t-- > 0) {
            ans = ans * sLoose * zLoose;
        }
        return ans;
    }
}