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 Archer {
	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();
		
		// Pr[SmallR wins] = p(sum_i=0^INF (1-p)^i*(1-q)^i)
		double p = (double) a / b;
		double q = (double) c / d;
		
		double prob = p;
		double r = 1.0;
		while (p * r > 1e-9) {
			r *= (1.0 - p) * (1.0 - q);
			prob += p * r;
		}
		
		System.out.printf("%.9f\n", prob);
		
		in.close();
		System.exit(0);
	}
}