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 = [int(i) for i in raw_input().strip().split()]

p = 0
psh = float(a) / float(b)
psm = float(b-a) / float(b)
pzh = float(c) / float(d)
pzm = float(d-c) / float(d)
for i in range(1000000):
    p += psh * psm**i * pzm**i

print p