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:
args = list(map(float, input().split(' ')))
a, b, c, d = args[0], args[1], args[2], args[3]
ab = a/b
cd = c/d
acbd = (a*c)/(b*d)
total=0
for i in range(100000):
    total += ab*((1-ab-cd+acbd)**i)

print(total)