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.*;
import java.math.BigInteger;

public class Solution{ 
	
		
	 
	 public static void main(String[] args) { 
	     
	     Scanner in = new Scanner(System.in);
	     StringBuilder sb=new StringBuilder();
	     
	     int a,b,c,d;
	     double p,q,answer;
	     
	     a=Integer.parseInt(in.next());
	     b=Integer.parseInt(in.next());
	     c=Integer.parseInt(in.next());
	     d=Integer.parseInt(in.next());
	    
	     p=(double)a/b;
	     q=(double)c/d;
	     
	     answer=p/(p+q-p*q);
	     
	     System.out.println(answer);
	     
	     
	     
	 }
}