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:
def read():
    return map(float, raw_input().strip().split(' '))

a,b,c,d=read()

e=0
archer=0
#A+ ~A~BA+ ~A~B~A~BA+..........
archer_prob = a/b
common_ratio = (b-a)/b*(d-c)/d

archer=archer_prob/(1-common_ratio)

print archer