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 gen(a, b):
	for i in range(b):
		yield (a**i)

line = input().split(" ")
a = 1 - int(line[0]) / int(line[1])
b = 1 - int(line[2]) / int(line[3])

print(sum(gen(a*b, 10000)) * (1 - a))