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.Scanner;

public class SolutionProb {

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int a = scanner.nextInt(), b = scanner.nextInt(), c = scanner.nextInt(), d = scanner.nextInt();
        double aWin = (a * 1.0) / b;
        double aLose = 1.0 - aWin;
        double bLose = 1.0 - (c * 1.0) / d;
        double prev = 0;
        double result = aWin;
        double acc = 1;
        while (((long)(prev * 100_000_000_000L)) != ((long) (result * 100_000_000_000L))) {
            acc *= aLose * bLose;
            prev = result;
            result += acc * aWin;
        }
        System.out.println(String.format("%.7f", result));
    }
}