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;

public class Archer {

	/**
	 * @param args
	 *            1 3 2 3
	 */
	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 x = (double)a / b;
		double y = (double)c / d;
		System.out.println(x / (1 - (1-x) * (1-y)));
	}

}