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.IOException;
import java.io.InputStreamReader;

public class cp {


  public static void main(String[] args) throws NumberFormatException, IOException {
    InputStreamReader ir = new InputStreamReader(System.in);
    BufferedReader br = new BufferedReader(ir);
    //String s=br.readLine();
    //String s1[]=br.readLine().trim().split(" ");
    //String s1[]=br.readLine().trim().split(" ");
    //int t1 = Integer.parseInt(br.readLine());
    String s1[]=br.readLine().trim().split(" ");
    int a = Integer.parseInt(s1[0]);
    int b = Integer.parseInt(s1[1]);
    int c = Integer.parseInt(s1[2]);
    int d = Integer.parseInt(s1[3]);
    double a1 = 1.0 - a*1.0/b;
    double b1 = 1.0 - c*1.0/d;
    System.out.println((a*1.0/b)*(1/(1.0 - a1*b1)));


  }


}