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:
s = raw_input()
a = [float(x) for x in s.split()]

#print(a)

# a[0] + (1 - a[0])/a[1]*(1 - a[2])/a[3]*a[0] + ...
# = a[0]/a[1]* geom(1 - a[0]/a[1])*(1 - a[2]/a[3])

ans = a[0]/a[1] * (1 / (1 - (1 - a[0]/a[1])*(1 - a[2]/a[3])) )
print(ans)