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:
s=input().split()

a=int(s[0])
b=int(s[1])
c=int(s[2])
d=int(s[3])

x=a/b
y=(1-x)*(c/d)

for i in range(10000):
    x+=(1-(x+y))*(a/b)
    y+=(1-(x+y))*(c/d)

print(x)