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 zip_sorted(a,b):

	# sorted  by a
	a,b = zip(*sorted(zip(a,b)))
	# sorted by b
	sorted(zip(a, b), key=lambda x: x[1])

	return a,b

import sys
input = sys.stdin.readline
I = lambda : list(map(int,input().split()))
S = lambda : list(map(str,input().split()))


a,b,c,d = I()
sum1 = (a/b)
sum2 = (a/b)
x = (1-(a/b))*(1-(c/d))
for i in range(10**6):
	sum2 = sum2*x
	sum1 = sum1 + sum2
print(sum1)