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()
r1 = int(a[0]) / int(a[1])
r2 = int(a[2]) / int(a[3])

q = (1-r1)*(1-r2)
s = (1-q**10000)/(1-q)
print( r1*s)