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 java.io.*;
public class Archer
{
	public static void main(String[] args)
	{
		Scanner in = new Scanner(System.in);
		
		int a = in.nextInt();
		int b = in.nextInt();
		int c = in.nextInt();
		int d = in.nextInt();
		
		double e = (double)a / b;
		double f = (double)c / d;
		
		double result = (double)a / b;
		double current = 1 - result;
		for(int x = 0; x < 1000000; x++)
		{
			current *= 1 - f;
			result += current * e;
			current *= 1 - e;
		}
		
		System.out.println(result);
	}
}