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 = tuple(map(float, raw_input().split()))

R = a/b
notR = 1 - R
Z = c/d
notZ = 1 - Z

EPS = 10 ** 6

ans = 0
for i in xrange(EPS):
    ans += (notR*notZ)**i * R

print ans