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.*;
public class archer {
    public static void main (String [] args) {
        Scanner kb = new Scanner (System.in);
        double a = kb.nextInt();
        double b = kb.nextInt();
        double c = kb.nextInt();
        double d = kb.nextInt();
        double output = (a * d) / (a * d + b * c - a * c);
        System.out.println(output);
    }
}