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:
z=raw_input()
z=z.split()
a=float(z[0])
b=float(z[1])
c=float(z[2])
d=float(z[3])
q=a/b;
s=c/d;
if (q==1):
	print 1
elif (s==1):
	print q;
else:
	r=(1-q)*(1-s);
	print (q)/(1-r)
#print a,b,c,d,q,r