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

def main():
	a,b,c,d = map(int, sys.stdin.readline().split())
	a = 1.0 * a
	c = 1.0 * c
	print (a / b) / (1 - (1 - a / b) * (1 - c / d))
if __name__ == "__main__":
	main()