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:
a, b, c, d = map(float, raw_input().split())
p1 = a/b
np1 = 1.0 - p1
p2 = c/d
np2 = 1.0 - p2
cur_p = p1
old_p = 0.0
i = 1
while True:
    old_p = cur_p
    cur_p += np1**i * np2**i * p1
    i += 1
    #print cur_p, old_p
    if cur_p - old_p < 0.000000001:
        break
print cur_p