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.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.Scanner;

public class Main {

    private static final InputStreamReader standardInput = new InputStreamReader(System.in);
    private static final BufferedReader bufferedReader = new BufferedReader(standardInput);
    private static final Scanner scanner = new Scanner(bufferedReader);

    private static final OutputStreamWriter standardOutput = new OutputStreamWriter(System.out);
    private static final BufferedWriter bufferedWriter = new BufferedWriter(standardOutput);
    private static final PrintWriter printWriter = new PrintWriter(bufferedWriter);

    public static void main(String[] args) {
        double a = scanner.nextDouble();
        double b = scanner.nextDouble();
        double c = scanner.nextDouble();
        double d = scanner.nextDouble();
        printWriter.print(getProbSmallRWins(a, b, c, d));
        printWriter.flush();
        scanner.close();
    }

    private static double getProbSmallRWins(double a, double b, double c, double d) {
        double num = a * b * d;
        double den = b * (b * d - (b - a) * (d - c));
        return num / den;
    }
}