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) {
		Scanner input = new Scanner(System.in);
		int a = input.nextInt(), b = input.nextInt(), c = input.nextInt(), d = input.nextInt();
		double A = a / (b * 1.0);
		double C = c / (d * 1.0);
		double B = (1 - A) * (1 - C);
		System.out.println(A / (1 - B));
	}

}