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.Scanner;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintStream;
import java.io.PrintWriter;
import java.math.*;

public class Main3{

	public static void main(String[] args) throws Exception {
    
		BufferedReader k=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer str=new StringTokenizer(k.readLine());
		int a=Integer.parseInt(str.nextToken());
        int b=Integer.parseInt(str.nextToken());
        int c=Integer.parseInt(str.nextToken());
        int d=Integer.parseInt(str.nextToken());
          double x=a*1.0/b*1.0;
          double y=c*1.0/d*1.0;
          y=(1-x)*(1-y);
          double sum=0;
          for (int i = 0; i < 7000; i++) {
			sum+=Math.pow(y, i)*x;
		}
        
        System.out.println(sum);
        
//!result2.equals("lala.")
		//result1.equals("miao.")
}

	
}