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[]){
        Solver s=new Solver();
        s.run();
    }
}



class Solver {
    PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
    FastReader in=new FastReader();
    public long pow(long a, long b){
        long ans=1;
        while(b>0){
            if(b%2==1){
                ans*=a;
            }
            a*=a;
            b/=2;
        }
        return ans;
    }
    public int gcd(int a, int b){
        while (b>0) {
            a %= b;
            int temp=b;
            b=a;
            a=temp;
        }
        return a;
    }
    public int[] getIntArray(int n){
        int arr[]=new int[n];
        for(int i=0;i<n;i++){
            arr[i]=in.nextInt();
        }
        return arr;
    }


    int mod=(int)1e9 +7;

    public void solve(){
        int a=in.nextInt(), b=in.nextInt(), c=in.nextInt(), d=in.nextInt();
        double alpha=a, beta=c;
        alpha/=b;beta/=d;
        double ans=0, temp=alpha, pk=alpha;

        do{
            ans+=pk;
            pk=pk*(1-alpha)*(1-beta);
            temp+=pk;
            // System.out.println(pk);
        }while(Math.abs(ans-temp)>1e-9);
        out.print(ans);
    }

    public void run(){
        int t=1;
        for(int i=0;i<t;i++){
            solve();
            out.println();
        }
        out.close();
    }
}
    
    
class FastReader { 
    final private int BUFFER_SIZE = 1 << 16; 
    private DataInputStream din; 
    private byte[] buffer; 
    private int bufferPointer, bytesRead; 
    
    public FastReader() { 
        din = new DataInputStream(System.in); 
        buffer = new byte[BUFFER_SIZE]; 
        bufferPointer = bytesRead = 0; 
    } 
    
    public FastReader(String file_name) throws IOException{ 
        din = new DataInputStream(new FileInputStream(file_name)); 
        buffer = new byte[BUFFER_SIZE]; 
        bufferPointer = bytesRead = 0; 
    } 
    
    public String nextLine() { 
        try{
            byte[] buf = new byte[10000]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        }catch (Exception e){
            System.out.println(e.getMessage());
            return null;
        }
    } 
    
    public int nextInt()  { 
        int ret = 0; 
        try {
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) c = read(); 
            do{ 
                ret = ret * 10 + c - '0'; 
            } while ((c = read()) >= '0' && c <= '9'); 
            if (neg) return -ret; 
            return ret; 
        } catch (Exception e) {
            System.out.println(e.getMessage());
                return -1;
            }
        } 
    
    public long nextLong()   {         
        try {
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret;
        } catch (Exception e) {
            System.out.println(e.getMessage());
            return -1;
        }
    }
    
    public double nextDouble()  {
        try {
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) c = read();     
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (c == '.') { 
                while ((c = read()) >= '0' && c <= '9') { 
                    ret += (c - '0') / (div *= 10); 
                } 
            } 
            if (neg) return -ret; 
            return ret;
        } catch (Exception e) {
            System.out.println(e.getMessage());
            return -1;
        }
    } 
    
    private void fillBuffer() throws IOException{ 
        bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
        if (bytesRead == -1) 
            buffer[0] = -1; 
    } 
    
    private byte read() throws IOException  { 
        try{
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
            }catch(Exception e){
                System.out.println(e.getMessage());
                return -1;
            }
        } 
    
    public void close() throws IOException { 
        if (din == null) 
            return; 
        din.close(); 
    } 
} 


    // class FastReader {
    //     BufferedReader br;
    //     StringTokenizer st;
    
    //     public FastReader() {
    //         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;
    //     }
    // }