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 traceback

try:
	eps = 10e-12
	a,b,c,d = map(float, raw_input().split())
	
	ak = a/b
	sum = a/b
	q = (1-a/b)*(1-c/d)
	
	while ak > eps:
		ak *= q
		sum += ak
		
	print sum
	
	#raw_input()
except:
	traceback.print_exc()
	raw_input()