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.util.Scanner;

/**
 * Created by kate on 09/01/15.
 */
public class Archer {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        double s = sc.nextDouble()/sc.nextDouble();
        double nz = 1 - sc.nextDouble()/sc.nextDouble();
        double ns = 1 -s;
        double p = s;
        double res = p;
        int n = 1;
        while (p >= 0.000000001) {
            p = 1;
            for (int i = 0; i < n; i++) {
                p *= ns*nz;
            }
            p *= s;
            n++;
            res += p;
        }
        System.out.println(res);
    }
}