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.*;


 
	public class test {
			
				public static  void main(String args[]) {
					Scanner sc=new Scanner(System.in);
					int a=sc.nextInt();
					int b=sc.nextInt();
					int c=sc.nextInt();
					int d=sc.nextInt();
					
					double ans=a*d;
					ans/=(b*c+a*d-a*c);

					System.out.printf("%.12f",ans);
							
	}

	}