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;


public class archer {
    public static void main(String[]args) throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String in = br.readLine();
        String [] p = in.split(" ");
        int a = Integer.parseInt(p[0]);
        int b = Integer.parseInt(p[1]);
        int c = Integer.parseInt(p[2]);
        int d = Integer.parseInt(p[3]);
        double aa = a*1.0/b;
        double bb = c*1.0/d;
        System.out.println(aa/(1-(1-aa)*(1-bb)));
    }

}