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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Scanner;

public class template
{

	public static ArrayList<Integer> strToInts(String str, String token)
	{
		ArrayList<Integer> result = new ArrayList<>();
		ArrayList<String> strs = new ArrayList<>(Arrays.asList(str.split(token)));
		for (String string : strs)
		{
			result.add(Integer.parseInt(string));
		}
		return result;
	}

	public static void main(String[] args) throws IOException
	{
		// The input and output streams
		 BufferedReader in = new BufferedReader(new InputStreamReader(System.in)); // system
		//BufferedReader in = new BufferedReader(new FileReader("input.txt"));
		 // File
		BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
		
		ArrayList<Integer> params = strToInts(in.readLine(), " ");
		double hitA = (double)params.get(0) / params.get(1);
		double hitB = (double) params.get(2) / params.get(3);
		double win = hitA;
		double newRound = (1 - hitA) * (1-hitB);
		int i = 0;
		while (true)
		{
			double newWin = newRound* (hitA);
			double newNewRound = newRound * (1 - hitA) * (1-hitB);
			newRound = newNewRound;
			if (newWin < 0.0000000001)
			{
				break;
			}
			else
				i++;
			win += newWin;
		}
		System.out.println(win);
		
	}







}