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.*;
import javax.swing.JOptionPane;

public class Solution {
	
	public static void main(String args[])
	{
		Scanner in = new Scanner(System.in);
		long a,b,c,d;
		a = in.nextLong();
		b = in.nextLong();
		c = in.nextLong();
		d = in.nextLong();
		double p = (double)a/b;
		double q = (double)c/d;
		double r = (1-p)*(1-q);
		double ans = p/(1-r);
		System.out.printf("%.9f\n",ans);
	}

}