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 scan = new Scanner(System.in);
		//MAC 2312
		double a = scan.nextDouble();
		double b = scan.nextDouble();
		double c = scan.nextDouble();
		double d = scan.nextDouble();
		double ans = (a/b)/(1-((b-a)/b*(d-c)/d));
		System.out.println(ans);
	}
}