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.util.*;
import java.lang.*;
import java.io.*;
import java.math.*;
import java.util.concurrent.*;

public class Main {
    //---------------------------------------------------------------------------
    
    
    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
        //-----------------------------------------------------------------------
        int a = in.nextInt();
        int b = in.nextInt();
        int c = in.nextInt();
        int d = in.nextInt();
        double x = (double)a / b;
        double y = (double)c / d;
        double lose = 1.0;
        double win = 0.0;
        for (int i = 0; i < 1000000; i++) {
            win += lose * x;
            lose *= (1.0 - x) * (1.0 - y);
        }
        out.printf("%.15f\n", win);
        //-----------------------------------------------------------------------
        out.close();
    }

    //---------------------------------------------------------------------------
    static void shuffleArray(int[] ar) {
        Random rnd = ThreadLocalRandom.current();
        for (int i = ar.length - 1; i > 0; i--) {
            int index = rnd.nextInt(i + 1);
            int a = ar[index];
            ar[index] = ar[i];
            ar[i] = a;
        }
    }

    static class Pair implements Comparator {

        long first, second, id;

        public Pair() {

        }

        public Pair(int f, int s, int i) {
            this.first = f;
            this.second = s;
            this.id = i;
        }

        @Override
        public int compare(Object o1, Object o2) {
            Pair p1 = (Pair) o1;
            Pair p2 = (Pair) o2;
            return Long.compare((long) p1.first * p1.second, (long) p2.first * p2.second);
        }
    }

    static class InputReader {

        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

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

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

        public char[] nextCharArray() {
            return next().toCharArray();
        }

        public boolean hasNext() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    String s = reader.readLine();
                    if (s == null) {
                        return false;
                    }
                    tokenizer = new StringTokenizer(s);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return true;
        }

        public void skipLine() {
            try {
                tokenizer = null;
                reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
    }
}