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:
a,b,c,d = map(int,raw_input().split())
p1 = 1.0*a/b
p2 = 1.0*c/d
a1 = 0.0
a2 = 0.0
for i in xrange(1000000):
  p = (1.0-p1)**i*(1.0-p2)**i
  p11 = p * a / b
  p21 = p * (1.0 - p1) * p2
  if p > 1e-8:
    a1 += p11
  else:
    break
print "%.8f" % (a1)  

#p(a)=a/b; p(b)=(1-a/b)*c/d