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 PYTHON):

Solution:
str = raw_input() ;
f = [int(s) for s in str.split() if s.isdigit()]

a = f[0] ;
b = f[1] ;
c = f[2] ;
d = f[3] ;

if c == d:
	print "0"
else: 
	print (a*1.0/b)/(1.0 - (1.0 - (a*1.0/b))*(1.0 - (c*1.0/d)))