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.io.*;

public class Main312B
{
  static PrintWriter out=new PrintWriter(System.out);
  
  public static void main(String[] args) throws IOException
  {
    Scanner sc=new Scanner(System.in);
    int a=sc.nextInt();
    int b=sc.nextInt();
    int c=sc.nextInt();
    int d=sc.nextInt();
    double x=(1-((double)a)/b)*(1-((double)c)/d);
    double ans=(((double)(a))/b)*(1/(1-x));
    out.println(ans);
    out.flush();
      
        
    
  }
  static class Scanner
  {
    BufferedReader br;
    StringTokenizer tk=new StringTokenizer("");
    public Scanner(InputStream is) 
        {
      br=new BufferedReader(new InputStreamReader(is));
    }
        public int nextInt() throws IOException
        {
          if(tk.hasMoreTokens())
                return Integer.parseInt(tk.nextToken());
          tk=new StringTokenizer(br.readLine());
          return nextInt();
        }
        public long nextLong() throws IOException
        {
            if(tk.hasMoreTokens())
              return Long.parseLong(tk.nextToken());
            tk=new StringTokenizer(br.readLine());
            return nextLong();
        }
        public String next() throws IOException
        {
          if(tk.hasMoreTokens())
            return (tk.nextToken());
            tk=new StringTokenizer(br.readLine());
            return next();
        }
        public String nextLine() throws IOException
        {
          tk=new StringTokenizer("");
          return br.readLine();
        }
        public double nextDouble() throws IOException
        {
            if(tk.hasMoreTokens())
              return Double.parseDouble(tk.nextToken());
            tk=new StringTokenizer(br.readLine());
            return nextDouble();
        }
        public char nextChar() throws IOException
        {
            if(tk.hasMoreTokens())
              return (tk.nextToken().charAt(0));
            tk=new StringTokenizer(br.readLine());
            return nextChar();
        }
        public int[] nextIntArray(int n) throws IOException
        {
            int a[]=new int[n];
            for(int i=0;i<n;i++)
              a[i]=nextInt();
            return a;
        }
        public long[] nextLongArray(int n) throws IOException
        {
          long a[]=new long[n];
            for(int i=0;i<n;i++)
              a[i]=nextLong();
            return a;
        }
        public int[] nextIntArrayOneBased(int n) throws IOException
        {
          int a[]=new int[n+1];
            for(int i=1;i<=n;i++)
              a[i]=nextInt();
            return a;
        }
        public long[] nextLongArrayOneBased(int n) throws IOException
        {
          long a[]=new long[n+1];
          for(int i=1;i<=n;i++)
                a[i]=nextLong();
          return a;
        }
  }
}