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=input().split(" ")
p=int(a[0])
q=int(a[1])
r=int(a[2])
s=int(a[3])
a=p/q
b=r/s
a=1-a
b=1-b
x=a*b
x=1-x
x=1/x
a=p/q
x=x*a
print(x)