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.io.*; 
import java.util.*; 
import java.lang.*;

public class code
{
	public static void main(String args[])throws IOException
	{
		Scanner scn = new Scanner(System.in);

		double a = scn.nextDouble();
		double b = scn.nextDouble();
		double c = scn.nextDouble();
		double d = scn.nextDouble();

		double p1 = a/b;
		double p2 = c/d;


		System.out.println(1/(1+ p2/p1 - p2));
	}	
}