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.util.Scanner;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;   

public class Archer {

	public static void main(String[] args) throws IOException {
		//get input separately
		Scanner scanner = new Scanner(System.in);
		int num1 = scanner.nextInt();
		int den1 = scanner.nextInt();
		int num2 = scanner.nextInt();
		int den2 = scanner.nextInt();
		
		double sr = (double)num1 / den1;
		double za = (double)num2 / den2;
		
		double prob = sr;
		double currProb = 0;
		int counter = 1;
		do {
			currProb = Math.pow((1 - sr) *  (1 - za), counter) * sr;
			prob += currProb;
			counter++;
		} while (currProb > Math.pow(10, -10));
		System.out.printf("%.7f %n", prob);

	}
	
	

}