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(float, raw_input().strip().split())
# \sum_{n=0}^{\inf} (1-a/b)^i(1-c/d)^i*a/b = a/b*(1/(1-r)),
r = (1.0 - a/b)*(1.0 - c/d)

print a/b*(1/(1-r))