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.*;

public class Main {
    public static void main(String[] args) throws IOException {
        MyScanner scn = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
        // Solution Start
        /*
        int t = scn.nextInt();
        while (t-- > 0) {
            solve(scn, out);
        }
        */
        double a = scn.nextDouble();
        double b = scn.nextDouble();
        double c = scn.nextDouble();
        double d = scn.nextDouble();
        double p1 = a / b;
        double p2 = c / d;
        double ans = 0;
        for (int i = 0; i < 10000; i++) {
            ans += Math.pow(1 - p1, i) * Math.pow(1 - p2, i) * p1;
        }
        out.println(ans);
        //Solution end
        out.close();
    }

    public static void solve(MyScanner scn, PrintWriter out) {
        long c = scn.nextLong();
        long sum = scn.nextLong();
        long r = sum % c;
        long d = sum / c;
        long cost = (d + 1) * (d + 1) * r + d * d * (c - r);
        out.println(cost);
    }

    public static long gcd(long x, long y) {
        if (y == 0) return x;
        else return gcd(Math.min(x, y), Math.max(x, y) % Math.min(x, y));
    }

    //-----------PrintWriter for faster output---------------------------------
    public static PrintWriter out;

    //-----------MyScanner class for faster input----------
    public 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());
        }

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

    }
    //--------------------------------------------------------
}