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:
string = input()
input_list = string.split(' ')

a = int(input_list[0])
b = int(input_list[1])
c = int(input_list[2])
d = int(input_list[3])

smallR_hit = a / b
zanoes_hit = c / d
not_smallR_hit = 1 - smallR_hit
not_zanoes_hit = 1 - zanoes_hit

print(smallR_hit / (1 - not_smallR_hit*not_zanoes_hit))