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:
from sys import stdin, stdout,stderr
import time,math
from collections import defaultdict as dd
 
def pn(ob):stdout.write(str(ob))
def inp():return stdin.readline()

def process():
	a, b, c, d = map(int, input().split())
	_s = 1 - (a/b)
	_z = 1 - (c/d)
	s = a/b;
	p = _s*_z;
	res = (1/(1-p))
	res = s * res	

	print(res)
 
def main():
	t=1
	#t=int(inp())
	start = time.time()
 
	while (t>0):
		t-=1
		process()
	end = time.time()
	#stderr.write('\nelapsed time'+str(end - start))
  
if __name__ == '__main__':
	main()
	
#n,m=map(int,input().split()) 
# for i in range(n):
#     t=int(stdin.readline()) # input using fast i/p method 
#     if t%m == 0:
#         stdout.write(str(t)+'\n') #input using fast o/p method
 
# take line of integers as input
# 	arr = list(map(int, inp().split()))