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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.lang.*;
import java.math.BigInteger;
public class test {
	 static ArrayList<Integer> primes;
	    static boolean[] isPrime;

	public static void main (String [] test)   {
		Scanner in = new Scanner (System.in);
		double a = in.nextDouble();double b = in.nextDouble();double c = in.nextDouble();double d = in.nextDouble();
		double proofa = a/b;
		double proofb = c/d;
		double conste = 1-(1-proofa)*(1-proofb);
		System.out.printf("%.10f",proofa/conste);
	
	  }
	  
	

}