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.*;
import java.math.*;
import static java.lang.Math.*;
import static java.lang.Integer.*;




public class B185 {
	int INF = Integer.MAX_VALUE / 100;
	static Scanner sc = null;
	static BufferedReader br = null;
	static PrintStream out = null;
	static BufferedWriter bw = null;
	int N = 0;
	
	public void solve() throws Exception{
		double a = sc.nextInt();
		double b = sc.nextInt();
		double c = sc.nextInt();
		double d = sc.nextInt();		
	
		double my = a / b;
		double you = c / d;
		
		double ans = 0;
		double rem = 1.0;
		while(true){
			if(rem < 0.00000001){
				break;
			}
			double now = rem * my;
			ans += now;
			rem -= now;
			now = rem * you;
			rem -= now;
		}
		out.println(ans);
	}
	

    public int[] readIntArray(int n) {
        int[] ret = new int[n];
        for (int i = 0; i < n; i++) {
            ret[i] = sc.nextInt();
        }
        return ret;
    }

	
	/**
	 * @param args
	 */
	public static void main(String[] args) throws Exception{
		File file = new File("input.txt");
		if(file.exists()){
			System.setIn(new BufferedInputStream(new FileInputStream("input.txt")));
		}
		out = System.out;
		bw = new BufferedWriter(new PrintWriter(out));
		sc =  new Scanner(System.in);
		//br = new BufferedReader(new InputStreamReader(System.in));
		B185 t = new B185();
		t.solve();
		bw.close();
	}

}