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.*;
import java.util.StringTokenizer;

public class Solution {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
        String str = br.readLine();
        StringTokenizer st = new StringTokenizer(str, " ");
        int a = Integer.parseInt(st.nextToken());
        int b = Integer.parseInt(st.nextToken());
        int c = Integer.parseInt(st.nextToken());
        int d = Integer.parseInt(st.nextToken());
        double num = (a * 1.0) / b;
        double deno = 1 - ((b - a * 1.0) / b * (d - c * 1.0) / d);
        bw.write(num / deno + "\n");
        bw.flush();
    }
}