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.math.BigDecimal;
import java.math.MathContext;
import java.math.RoundingMode;
import java.util.Arrays;
import java.util.Scanner;


public class Main {
    
    
    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringBuilder out = new StringBuilder();
        int a = sc.nextInt();
        int b = sc.nextInt();
        int c = sc.nextInt();
        int d = sc.nextInt();
        
        double ans = 0;
        double res = (a *1.0)/b;
        double se = (c *1.0)/d;
        double fe = (a *1.0)/b;
        double th = (1-res) * (1 - se);
        while(Math.abs(ans - res) > 10e-10 ){
            ans = res;
            res += th * (a *1.0)/b;
            th *= (1-fe) * (1 - se);
        }
        
        System.out.println(res);
        
    }

}