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.*;
public	class	Main{
	public	static	void	main(String[]args)throws	Exception{
		Scanner	cin=new	Scanner(System.in);
		int	a=cin.nextInt(),b=cin.nextInt(),c=cin.nextInt();
		System.out.print(a/(c*(b-a)/cin.nextDouble()+a));
	}
}