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 PYTHON):

Solution:
import sys
s = sys.stdin.readline()
data = [int(word) for word in s.split(" ")]
a = data[0]
b = data[1]
c = data[2]
d = data[3]

smallR_win = a*1.0/b
Z_win = c*1.0/d

P = smallR_win / (1-(1-smallR_win)*(1-Z_win))
print P