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())
fail = (float(b - a) / b) * (float(d - c) / d)
res = 0.0
i = 0
while True:
  inc = (fail ** i) * (float(a) / b)
  res += inc
  if inc < 1e-15: break
  i += 1
print res