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 TestClass 
{
    public static void main(String[] args) throws Exception {

	    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        OutputStream outputStream = System.out;
    	PrintWriter out = new PrintWriter(outputStream);

	    int i, j, k;
        
        StringTokenizer st = new StringTokenizer(br.readLine());
        double a = Integer.parseInt(st.nextToken());
        double b = Integer.parseInt(st.nextToken());
        double c = Integer.parseInt(st.nextToken());
        double d = Integer.parseInt(st.nextToken());
        
        out.print((a/b)/(1-(1-(a/b))*(1-(c/d))));
        out.flush();
	    out.close();
	}
}