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 sc = new Scanner(System.in);
      double a = sc.nextInt();
      double b = sc.nextInt();
      double c = sc.nextInt();
      double d = sc.nextInt();
      double ans = (a*d)/ (b*d - (b-a)*(d-c));
      System.out.println(ans);

   }
}