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.InputStreamReader;
import java.io.PrintWriter;
import java.util.Scanner;

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

    public static void main(String[] args) {
        Scanner in = new Scanner(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
        int a = in.nextInt();
        int b = in.nextInt();
        int c = in.nextInt();
        int d = in.nextInt();
        double err = 1e-9;
        double last = 0;
        double winA = (double) a / b;
        double winB = (double) c / d;
        double result = winA;
        double prev = 1;
        while(result - last >= err){
            prev *= (1 - winA)*(1 - winB);
            last = result;
            result += prev*winA;                        
        }
        out.println(result);
        out.close();

    }

    public double pow(double a, int b) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        double val = pow(a, b / 2);
        if (b % 2 == 0) {
            return val * val;
        } else {
            return val * val * a;
        }
    }

    public static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    public static long lcm(long a, long b) {
        return a * b / gcd(a, b);
    }
}