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.*;
public class j
{
public static void main(String aa[])throws IOException
{
BufferedReader b=new BufferedReader(new InputStreamReader(System.in));
int i=0,m=0,n=0,k=0,p=0,l=0;
double t=0;
String s;
s=b.readLine();
StringTokenizer c=new StringTokenizer(s);
m=Integer.parseInt(c.nextToken());
n=Integer.parseInt(c.nextToken());
k=Integer.parseInt(c.nextToken());
l=Integer.parseInt(c.nextToken());
t=((1.0/(1-((1-(double)m/n)*(1-(double)k/l))))*((double)m/n)*(1-(double)m/n)*(1-(double)k/l))+((double)m/n);
System.out.print(t);
}
}