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 main 
{
	public static void main(String[] args) throws Exception
	{
		Scanner in = new Scanner(System.in);
		
		int a = in.nextInt();
		int b = in.nextInt();
		int c = in.nextInt();
		int d = in.nextInt();
		
		double hit = (double) a / (double) b;
		double miss = 1 - hit;
		double omiss = 1 - ((double) c / (double) d);
		
		double startChance = hit;
		double missChance = miss * omiss;
		
		double ans = 0;
		
		while(startChance >= .000000001)
		{
			ans += startChance;
			
			startChance = missChance * hit;
			missChance = missChance * miss * omiss;
		}
		
		System.out.println(ans);
	}
}