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())
result = 0
small = a/b
small_wrong = 1 - small
zanos_wrong = 1 - (c/d)
both_wrong = small_wrong * zanos_wrong
for i in range(1, 100000):
    result += (small) * (both_wrong**(i - 1))
print result