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 = list(map(int, input().split()))
R = a/b
Z = c/d
final = 0
p_atual = 1
# print(a,b,c,d)
for i in range(10000):
    final += p_atual * (1-R) * Z
    p_atual = p_atual * (1-R) * (1-Z)

print(1-final)