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:
a,b,c,d = [int(x) for x in input().split()]

p_smallR = a/b
p_zanoes = c/d

trials = 100000

smallR_wins = 0
zanoes_wins = 0
cur_prob = 0

for n in range(trials):
    cur_prob += p_smallR * ((1 - p_smallR) * (1 - p_zanoes)) ** n
    
        
print(cur_prob)