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 _312B {

	static Scanner scanner = new Scanner(System.in);
	static double a, b, c, d, p1, p2, sum, delta;

	public static void main(String[] args) {
		a = scanner.nextDouble();
		b = scanner.nextDouble();
		c = scanner.nextDouble();
		d = scanner.nextDouble();
		p1 = a / b;
		p2 = c / d;
		sum = 0.0;
		for (int i=1;;i++) {
			delta = Math.pow(1-p1, i-1) * p1 * Math.pow(1-p2, i-1);
			if (delta < 10e-15) {
				System.out.println(sum);
				break;
			}
			else {
				sum += delta;
			}
		}

	}

}