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 past_conts {

	public static void main(String[] args) {
		Scanner sc=  new Scanner(System.in);double a = sc.nextDouble();double b = sc.nextDouble();double c = sc.nextDouble();double d = sc.nextDouble();
	    	double p1 = a/b;
	    	double p = (1-p1)*(1-(c/d));
	    	double prop = p1/(1-p);
	    	System.out.println(prop);
	}
}