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())

eps = 1e-12

p = 0
pre = 1.
while True:
    delta = 1.0 * pre * a / b 
    if delta < eps:
        break
    pre = pre * (b - a) / b * (d - c) / d
    p += delta
print(p)