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 Test2 {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub

		Scanner s=new Scanner(System.in);
		int a,
			b,
			c,
			d;
		
		double ver;
		a=s.nextInt();
		b=s.nextInt();
		c=s.nextInt();
		d=s.nextInt();
		
		
		double n=(double)a/b;
		double m=(double)c/d;
		
		
		
		ver=n/(1-(1-n)*(1-m));
		
		System.out.println(ver);
		
		
		
	}

}