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:
//package contest312;

import java.util.Scanner;

public class Main {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		double a, b, c, d, p, q, res;
		Scanner in = new Scanner(System.in);
		a = in.nextDouble();
		b = in.nextDouble();
		c = in.nextDouble();
		d = in.nextDouble();
		p = a/b;
		q = c/d;
		res = p;
		for(int i=1; ; i++) {
			double temp = Math.pow(1-p, i)*Math.pow(1-q, i)*p;
			if(temp < Math.pow(10, -12)) break;
			res += temp;
		}
		System.out.printf("%.12f", res+5.0*Math.pow(10, -13));
	}

}