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:
from decimal import Decimal
a, b, c, d = map(Decimal, input().split())
previous = -1
current = 0
i = 0
q = a / b
r = c / d

while abs(current - previous) > 1e-9:
    previous = current
    current += q *( ((1 - r)*(1 - q)) ** i)
    i += 1
print(current)