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.HashSet;
import java.util.Set;
import java.util.StringTokenizer;
     
     
     
    public class App {
    	static class FastReader {
    		BufferedReader br;
    		StringTokenizer st;
     
    		public FastReader() {
    			br = new BufferedReader(new InputStreamReader(System.in));
    		}
     
    		String next() {
    			while (st == null || !st.hasMoreElements()) {
    				try {
    					st = new StringTokenizer(br.readLine());
    				} catch (IOException e) {
    					e.printStackTrace();
    				}
    			}
    			return st.nextToken();
    		}
     
    		int nextInt() {
    			return Integer.parseInt(next());
    		}
     
    		long nextLong() {
    			return Long.parseLong(next());
    		}
     
    		double nextDouble() {
    			return Double.parseDouble(next());
    		}
     
    		String nextLine() {
    			String str = "";
    			try {
    				str = br.readLine();
    			} catch (IOException e) {
    				e.printStackTrace();
    			}
    			return str;
    		}
    	}
     
     
    	public static void main(String args[]) {
    		 FastReader sc = new FastReader();
    		//Scanner sc = new Scanner(System.in);
    		// System.out.println(java.time.LocalTime.now());
    		int a = sc.nextInt(), b = sc.nextInt(), c = sc.nextInt(), d = sc.nextInt();
    		
    		double ans = 1-((double)((b-a)*c)/(double)((b*d)-(b-a)*(d-c)));
    		System.out.printf("%.12f", ans);
    	}
    	
    }
     
     
    class Pair implements Comparable<Pair>{
    	public int ind;
    	public int num;
    	
    	Pair(int a, int b){
    		this.ind = a;
    		this.num = b;
    	}
     
     
    	@Override
    	public int compareTo(Pair o) {
    		return num-o.num;
    	}
    	
    }