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;


public class Prob312B
{
    public static void main( String[] Args )
    {
        Scanner scan = new Scanner( System.in );
        int a = scan.nextInt();
        int b = scan.nextInt();
        int c = scan.nextInt();
        int d = scan.nextInt();
        double r1 = a/1.0/b;
        double r2 = c/1.0/d;
        double r3 = (1-r1)*(1-r2);
        System.out.println(r1/(1-r3));
    }
}