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.*;
public class B312 {
	public static double p1, p2;
	public static void main(String[] args){
		Scanner br = new Scanner(System.in);
		p1 = br.nextDouble()/br.nextDouble();
		p2 = br.nextDouble()/br.nextDouble();
		System.out.println(go(0, 1.0));
	}
	public static double go(int turn, double prob){
		if(prob <= 1e-20){
			return 0;
		}
		if(turn == 0){
			return p1*1 + (1-p1)*go(1-turn, prob*(1-p1));
		}
		else{
			return (1-p2)*go(1-turn, prob*(1-p2));
		}
	}
}