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 abc
{
    public static void main(String ar[])
    {
        Scanner sc = new Scanner(System.in);
        int a=sc.nextInt(),b=sc.nextInt(),c=sc.nextInt(),d=sc.nextInt();
        double ans=(a*d*1.0)/((a*d*1.0)+(b*c*1.0)-(c*a*1.0));
        System.out.println(ans);
    }
}