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.*;
public class b
{
	public static void main(String[] args)
	{
		Scanner sc = new Scanner(System.in);
		double a = (double)sc.nextInt();
		double b = (double)sc.nextInt();
		double c = (double)sc.nextInt();
		double d = (double)sc.nextInt();
		double ans = 0;
		double temp = 1;
		for (int i = 1; i <= 500000;i++)
		{
			ans += temp * a / b;
			temp *= (1 - a / b) * ( 1 - c / d);
		}
		System.out.println(ans);

	}
}