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:
q = raw_input().split()
a = float(q[0])
b = float(q[1])
c = float(q[2])
d = float(q[3])

x = a/((a/b)+(c/d)-(a*c/b/d))/b
print x


"""
x = a/b + (1-a/b)(1-c/d)x

1-(1+ac/bd-a/b-c/d)x = a/b

(-ac/bd+a/b+c/d)x = a/b

"""