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 Main {

	public static class Solver {

		static final double N = 100100;
		double p;
		double q;

		private double calcProb(int idx) {
			if (idx == N)
				return 0;
			else
				return p + (1.0 - p) * q * calcProb(idx + 1);
		}

		public void solve() {
			Scanner scanner = new Scanner(System.in);
			int a = scanner.nextInt();
			int b = scanner.nextInt();
			int c = scanner.nextInt();
			int d = scanner.nextInt();
			scanner.close();
			p = a * 1.0 / b;
			q = 1.0 - c * 1.0 / d;
			System.out.println(calcProb(0));
		}
	}

	public static void main(String[] args) {
		Solver s = new Solver();
		s.solve();
	}
}