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.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Solution {
	public static void main(String[] args) {
		FastScanner fs=new FastScanner();
		int a = fs.nextInt(), b = fs.nextInt(), c = fs.nextInt(), d = fs.nextInt();
		
		double x = (double)a/(double)b;
		double y = 1.0 - x;
		
		double z = 1.0 - ((double)c/(double)d);
		
		double r = y * z;
		
		double ans = x/(1.0 - r);
		
		System.out.println(ans);
		//System.out.println(z);
    }
	
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		public String next() {
			while (!st.hasMoreElements())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		int[] readArray(int n) {
			int[] a=new int[n]; 
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		
		int nextInt () {
			return Integer.parseInt(next());
		}
		
		long nextLong() {
			return Long.parseLong(next());
		}
	}

}