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 PYTHON3):

Solution:
a, b, c, d = map(int, input().split())
"""
x = p1 + p3*x
0 = p1 + (p3-1)*x
-p1 = (p3-1)*x
p1 = (1-p3)*x
x = p1/(1-p3)

"""

p1 = a/b
p2 = c/d
p3 = (1-p1)*(1-p2)
print(p1/(1-p3))