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().strip().split())

x = a / (b*1.0)
xd = 1 - x
y = c / (d*1.0)
yd = 1 - y

p = x

term = xd*yd*x
while term > 10**-9:
    p += term
    term*=xd*yd
print p