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 Archer312B
{
    public static void main(String[] args) 
    {
        // Set up scanner
        Scanner sc = new Scanner(System.in); 
        // System.out.println("Enter a");
        int a = sc.nextInt();
        // System.out.println("Enter b");
        int b = sc.nextInt();
        // System.out.println("Enter c");
        int c = sc.nextInt();
        // System.out.println("Enter d");
        int d = sc.nextInt();
        
        double r = (double)a/b;
        double notr = 1-r;
        double s = (double)c/d;
        double nots = 1-s;
        
        double answer = 0.0;
        double newone = r;
        while (newone > 1.0E-12)
        {
            answer += newone;
            newone = notr*nots*newone;
        }
        System.out.println(answer);
    }
}