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 {
	
	
	
	public static void main(String args []) {
		InputReader obj = new InputReader(System.in);
		int a = obj.nextInt();
		int b = obj.nextInt();
		int c = obj.nextInt();
		int d = obj.nextInt();
		
		double t = 1.0*(1-1.0*a/b)*(1-1.0*c/d);
		double e = 1.0*(1.0*a/b)/(1-t);
		System.out.println(e);
	}
	public 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());
	    }
	    
 
	}
}