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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.HashSet;
import java.util.StringTokenizer;


public class codeforces {
	static PrintWriter out;
	public static void main(String[] args) {
		MyScanner scan = new MyScanner();
		out = new PrintWriter(System.out);
		
		double p = scan.nextDouble()/scan.nextDouble();
		double q = scan.nextDouble()/scan.nextDouble();
		out.println(p*(1./(1-((1-p)*(1-q)))));
		out.close();
	}

	private static class MyScanner {
		BufferedReader br;
		StringTokenizer st;
		public MyScanner() {br = new BufferedReader(new InputStreamReader(System.in));}
		String next(){
			while(st==null||!st.hasMoreElements()){
				try{st = new StringTokenizer(br.readLine());}
				catch(IOException e){e.printStackTrace();}
			}return st.nextToken();
		}
		int nextInt() {return Integer.parseInt(next());}
		long nextLong(){return Long.parseLong(next());}
		double nextDouble(){return Double.parseDouble(next());}
	}
}