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:
q = raw_input()

z = ["","","",""]

j = 0

for i in q:
    if i == " ":
     j += 1
    else:
     z[j] = z[j] + i

a = z[0]
b = z[1]
c = z[2]
d = z[3]

sum = 0

count = float(a)/float(b)
sum += count

x = float(a)/float(b)
y = float(c)/float(d)

for i in range(10000):
    count = count*(1- y)*(1-x)
    sum += count

print sum