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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

/*
 * To change this template, choose Tools | Templates
 * and open the template in the editor.
 */
/**
 *
 * @author 11x256
 */
public class Archer {

    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        String[] temps = in.readLine().split(" ");
        float a = Float.parseFloat(temps[0]);
        float b = Float.parseFloat(temps[1]);
        float c = Float.parseFloat(temps[2]);
        float d = Float.parseFloat(temps[3]);
        float x = a / b;
        float y = (1 - x) * (1 - (c / d));
        float res = x;
        for (int i = 1; i < 100000; i++) {
            res += x * Math.pow(y, i);
        }   
        System.out.printf("%.15f",res);
        System.out.println("");
    }
}