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.*;
import java.lang.*;
import java.math.BigInteger;


public class HelloWorld {
    InputReader input;
    PrintWriter output;
    void run(){
        output = new PrintWriter(new OutputStreamWriter(System.out));
        input = new InputReader(System.in);
        solve();
        output.flush();
    }
    
    
    public static void main(String[] args){
        new HelloWorld().run();
    }
    
    
    void solve() {
        int a = input.readInt();
        int b = input.readInt();
        int c = input.readInt();
        int d = input.readInt();
        double prob = (double)a / b;
        double z = (double)c / d;
        double r = (double)a / b;
        double rczc = (1 - z) * (1 - r);
        double cache = 1.00;
        for(int i = 0; i < 10000; i++) {
            cache = cache * rczc;
            prob += cache * r;
        }
        output.println(prob);
    }
    
    class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        public InputReader(InputStream stream) {
            this.stream = stream;
        }
        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars)
            {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
        public int readInt() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuffer res = new StringBuffer();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }
        public Long readLong() {
            return Long.parseLong(readString());
        }
        public Double readDouble() {
            return Double.parseDouble(readString());
        }
        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
    }
}