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.util.StringTokenizer;

public class Problem1 {

    public static void main(String[] args  ){

        MyScanner sc = new MyScanner();

        Double a,b,c,d;
        a = sc.nextDouble(); b = sc.nextDouble(); c = sc.nextDouble(); d = sc.nextDouble();
        Double x = (a/b)/(1-(1-(a/b))*(1-(c/d)));
        System.out.printf("%.7f",x);

    }

    public static class MyScanner{
        BufferedReader br;
        StringTokenizer st;

        public MyScanner(){
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next(){
            while (st == null || !st.hasMoreTokens() ){
                try{
                    st = new StringTokenizer(br.readLine());
                }
                catch (Exception ex){
                    ex.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt(){
            return Integer.parseInt(next());
        }

        long nextLong(){
            return Long.parseLong(next());
        }

        Double nextDouble(){
            return Double.parseDouble(next());
        }

        String nextLine(){
            String str = null;
            try{
                str = br.readLine();
            }
            catch (IOException ex){
                ex.printStackTrace();
            }
            return str;
        }

    }

}