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:
abcd = [int(i) for i in input().split()];

# убывающая прогрессия S= b1/(1-q)
# q = (1-a/b)*(1-c/d)
# b1 = a/b

print(abcd[0]/abcd[1]/ ( 1- (1-abcd[0]/abcd[1]) * (1-abcd[2]/abcd[3]) ))