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:
ans = 0.0
p = 1.0
id = input().split()
a, b, c, d = int(id[0]), int(id[1]), int(id[2]), int(id[3])
for i in range( 100000 ):
	ans += p * a / b
	p *= (1.0 - a / b)
	p *= (1.0 - c / d)
print( ans )