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 Main {
    
    BufferedReader in;
    StringTokenizer str = null;
    PrintWriter out;
    
    private String next() throws Exception{
	if (str == null || !str.hasMoreElements())
	    str = new StringTokenizer(in.readLine());
	return str.nextToken();
    }
    
    private int nextInt() throws Exception{
	return Integer.parseInt(next());
    }
    
    private long nextLong() throws Exception{
	return Long.parseLong(next());
    }
    
    private double nextDouble() throws Exception{
	return Double.parseDouble(next());
    }
    
    public void run() throws Exception{
	in =  new BufferedReader(new InputStreamReader(System.in));
	out = new PrintWriter(System.out);
	double a = nextDouble();
	double b = nextDouble();
	double c = nextDouble();
	double d = nextDouble();
	double r = 0;
	double p1 = 1;
	double p2 = 1;
	for(int i=0;i<10000;i++){
	    r+=a/b*p1*p2;
	    p1*=(b-a)/b;
	    p2*=(d-c)/d;
	}
	out.println(r);
	out.close();
    }
    
    public static void main(String[] args) throws Exception{
	new Main().run();
    }
}