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.math.*;
import java.security.*;
import java.text.*;
import java.util.*;
import javafx.util.Pair;

public  class CodeForce {
static	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
static StringBuilder sb = new StringBuilder();
static long gcd(long a, long b) 
{ 
  if (b == 0) 
    return a; 
  return gcd(b, a % b);  
} 
	static boolean flag = false;
	static int next(String [] sr,int ind)
	{
		return Integer.parseInt(sr[ind]);
	}

	public static void main(String[] args) throws IOException {
		
		//int t=Integer.parseInt(br.readLine());
		//while(t-->0)
	//	{
			
		String[] sr=br.readLine().split(" ");
		double a=Double.parseDouble(sr[0]);
		double b=Double.parseDouble(sr[1]);
		double c=Double.parseDouble(sr[2]);
		double d=Double.parseDouble(sr[3]);
		
		double x=(1-a/b)*(1-c/d);
		System.out.println((a/b)/(1-x));
		
		
		
		
		}
		
		
		
		
		
		
		
		
		
		
		
		
		
		
		
		
		
		
		
		
		
		
		
		
	}