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 Round185B {

    static Scanner sc = new Scanner(System.in);

    static int N;
    static int a;
    static int b;
    static int c;
    static int d;

    public static void main(String[] args) {
        read();
        solve();
    }

    public static void read() {
        a = sc.nextInt();
        b = sc.nextInt();
        c = sc.nextInt();
        d = sc.nextInt();
    }

    public static void solve() {
        double x = (double) a/b;
        double y = (double) c/d;

        double ans = 0;
        final int tries = 100000;
        ans += (1-x) * y;
        for (int i = 2; i <= tries; i++) {
            ans += Math.pow((1-x)*(1-y), (i-1)) * (1-x) * y;
        }

        System.out.println(1 - ans);
    }

    public static double fact(int n) {
        if (n == 0) return 1;
        else return n * fact(n-1);
    }
}