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 static java.lang.System.in;
import static java.lang.System.out;

import java.util.Scanner;


public class B312 {
	static long MAX = 1000000007;
	public static Scanner sc=new Scanner(in);
	public void run(){
		// TODO Auto-generated method stub
		int a=sc.nextInt(), b = sc.nextInt(), c=sc.nextInt(), d = sc.nextInt();
		b-=a;
		a*=d;
		ln((double)a/(double)(a+b*c));
	}
	
	public static void main(String[] args) {
		new B312().run();
	}
	public static void ln(Object obj){
		out.println(obj);
	}

}