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.InputStreamReader;

public class Solution {
    public static void main(String[] args) throws Exception {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));

        String[] inputStrings = reader.readLine().split(" ");

        double a = Integer.parseInt(inputStrings[0]);
        double b = Integer.parseInt(inputStrings[1]);
        double c = Integer.parseInt(inputStrings[2]);
        double d = Integer.parseInt(inputStrings[3]);

        double result = (a / b) / (1 - (1 - (a / b)) * (1 - (c / d)));

        System.out.println(result);
    }
}