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.*; //Scanner;
import java.io.PrintWriter; //PrintWriter

public class R185_Div2_B //Name: Archer
{
	public static void main(String[] args) {
		Scanner      in = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		solve(in, out);
		out.close();
		in.close();	
	}
	
	public static void solve(Scanner in, PrintWriter out)
	{
		double a = in.nextInt();	
		double b = in.nextInt();
		double c = in.nextInt();	
		double d = in.nextInt();
		
        double p = 0;
        for (int i = 0; i < 7000; i++)
        {
            double prod = 1.0;
            for (int j = 0; j < i; j++)
                prod *= (1.0 - a/b) * (1.0 - c/d);
            prod *= a / b;
            p += prod;
        }
		
		out.println(p);		
	}
}