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.math.*;
import java.util.*;

public class Main implements Runnable {
    private BufferedReader br;
    private StringTokenizer tok;
    private PrintWriter out;

    static final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;

    static final double EPS = 1e-12;

    void solve() throws IOException {
        int[] a = new int[4];

        for (int i = 0; i < 4; ++i) {
            a[i] = nextInt();
        }

        double pa = (a[0] + .0) / a[1],
               pb = (a[2] + .0) / a[3];

        double curP = pa;

        double res = 0;

        while (curP > EPS) {
            res += curP;
            curP /= pa;
            curP *= (1.0 - pa) * (1.0 - pb) * pa;
        }

        out.printf("%.9f", res);
    }

    public void run() {
        try {
            if (ONLINE_JUDGE) {
                br = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(System.out);
            } else {
                br = new BufferedReader(new FileReader(new File("input.txt")));
                out = new PrintWriter(new File("output.txt"));
            }
            solve();
            br.close();
            out.close();
        } catch (IOException e) {
            e.printStackTrace();
            System.exit(1);
        }
    }

    public static void main(String[] args) {
        new Thread(null, new Main(), "", 128 * (1L << 20)).start();
    }

    String nextToken() throws IOException {
        while (tok == null || !tok.hasMoreTokens())
            tok = new StringTokenizer(br.readLine());
        return tok.nextToken();
    }

    String nextString() throws IOException {
        return nextToken();
    }

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

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

    double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    BigInteger nextBigInteger() throws IOException {
        return new BigInteger(nextToken());
    }
}