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 hcl{
	public static void main(String[] args){
		int mod =1000003;
	  Scanner scan = new Scanner(System.in);
       int a= scan.nextInt();
       int b = scan.nextInt();
       int c = scan.nextInt();
       int d = scan.nextInt();
       double p = (double)a/b;
       double temp1 = 1-p;
     // System.out.println("reverse of temp1 = "+temp1);
       double temp2 = (double)c/d;
     //  System.out.println("2nd = "+temp2);
      double q = temp1*(1-temp2);
    //   System.out.println("q = "+q);
       double ans = p/(1-q);
       System.out.println(ans);

	}
}