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.File;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Scanner;
import static java.lang.Math.*;

public class Main {

	public static void main(String[] args) throws Exception {
		Scanner in = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		double a=in.nextDouble();
		double b=in.nextDouble();
		double c=in.nextDouble();
		double d=in.nextDouble();
		double pot=(a/b)/(1-(1-(a/b))*(1-(c/d)));
		System.out.println(pot);
	
	}

	private static void print(Object... rs) {
		System.err.println(Arrays.deepToString(rs).replace("],", "]\n"));
	}

}