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:
a, b, c, d = [int(i) for i in input().split()]

probs = a/b
nprobs = 1 - probs
probz = 1 - c/d

currentp = probs
accum = probs
oldp = 0

while currentp-oldp>0.000000001:
    oldp = currentp
    accum *= nprobs*probz
    currentp += accum

print(currentp)