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.*;
import java.io.*;


public class B {
	
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out); 
		int a = sc.nextInt();
		int b = sc.nextInt();
		int c = sc.nextInt();
		int d = sc.nextInt();
		sc.close();
		
		double ab = (double)a/(double)b;
		
		double cd = (double)c/(double)d;
		
		double x = (1-ab)*(1-cd);
		
		double res = ab/(1-x);
		
		out.println(res);
		out.flush();
	}
}