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.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.PrintWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.StringTokenizer;

public class Solver {

	public static void main(String[] Args) throws NumberFormatException,
			IOException {
		new Solver().Run();
	}

	PrintWriter pw;
	StringTokenizer Stok;
	BufferedReader br;

	public String nextToken() throws IOException {
		while (Stok == null || !Stok.hasMoreTokens()) {
			Stok = new StringTokenizer(br.readLine());
		}
		return Stok.nextToken();
	}

	public int nextInt() throws NumberFormatException, IOException {
		return Integer.parseInt(nextToken());
	}

	public double nextDouble() throws NumberFormatException, IOException {
		return Double.parseDouble(nextToken());
	}

	public long nextLong() throws NumberFormatException, IOException {
		return Long.parseLong(nextToken());
	}

	public void Run() throws NumberFormatException, IOException {
		//br = new BufferedReader(new FileReader("input.txt"));
		//pw = new PrintWriter("output.txt");
		br = new BufferedReader(new InputStreamReader(System.in));
		pw = new PrintWriter(new OutputStreamWriter(System.out));
		int a = nextInt(), b = nextInt(), c = nextInt(), d = nextInt();
		double v1 = (double) a / b, v2 = 1 - (double) c / d;
		double fin = (1-v1) * v2;
		pw.print(v1/(1-fin));
		pw.flush();
		pw.close();
	}

}