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.BigInteger;

public class A {

	static long[][] answer;
	
	public static void main(String args[]) throws Exception{
		Scanner in = new Scanner(System.in);
	
		int a = in.nextInt();
		int b = in.nextInt();
		int c = in.nextInt();
		int d = in.nextInt();
		
		double p = (double)a/b;
		double q = (double)c/d;
		
		int ctr = 0;
		double ans = 0;
		
		double term = 1;
		
		while( true ) {
			
			if( ctr != 0 ) { term *= (1-p)*(1-q); }
			else term *= p;
			
			if( term <= 0.0000000000001 ) break;
			
			ans += term;
			ctr++;
		}
		
		System.out.printf("%.12f\n", ans);
		
	}
}

// p and q
// p + (1-p)(1-q) * p + (1-p)(1-q)*(1-p)(1-q) * p