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:
n = input()
a,b,c,d = n.split()
a = float(a)
b = float(b)
c = float(c)
d = float(d)

start = a/b

r = (1-start)*(1- c/d)

ans = start/(1-r)

print(ans)