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:
def main():
	data = list(map(int, input().split()))
	accuracy_prob = data[0] / data[1]
	lose_prob = (1 - accuracy_prob) * (1 - data[2] / data[3])
	archer_prob = accuracy_prob / (1 - lose_prob)
	print(format(archer_prob,'.15f'))


if __name__ == '__main__':
	main()