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.*;
import java.util.StringTokenizer;

public class Main4 {
    PrintWriter out;
    BufferedReader input;

    Main4() {
        try {
            input = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter(new FileWriter("output.txt"), true);
            solver();
        } catch (Exception ex) {
            ex.printStackTrace();
            input = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out, true);
            solver();
        } finally {
            out.close();
            try {
                input.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
    }

    StringTokenizer st = new StringTokenizer("");

    private String nextToken() {
        while (!st.hasMoreElements()) {
            try {
                st = new StringTokenizer(input.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

    private int nextInt() {
        return Integer.parseInt(nextToken());
    }

    private long nextLong() {
        return Long.parseLong(nextToken());
    }

    public void solver() {
        int a = nextInt();
        int b = nextInt();
        int c = nextInt();
        int d = nextInt();
        double k = (1.0*a/b*(1-1.0*c/d)+1.0*c/d*(1-1.0*a/b)+(1.0*a/b)*(1.0*c/d));
        out.println((1.0*a/b)/k);
    }

    public static void main(String[] args) {
        new Main4();
    }
}