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:
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
  static int arr[];
  static void getPrimes(){
    Arrays.fill(arr,1);
    arr[1]=0;
    for(int i=2;i*i<arr.length;i++){
      if(arr[i]==1) {
        for (int j = i * 2;j<arr.length;j=j+i){
          arr[j]=0;
        }
      }
    }
  }
  public static void main (String[] args) {
    Scanner sc = new Scanner(System.in);
    double a=sc.nextDouble();double b=sc.nextDouble();
    double c=sc.nextDouble();double d=sc.nextDouble();

    System.out.printf("%.12f",(a*d)/(b*d - ((b-a)*(d-c))));
  }
}