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:
I=lambda:map(int, raw_input().split())
a,b,c,d=I()
p,q=float(a)/b,float(c)/d
inf=0.0000000001
ans,x=0.0,1.0
while x>inf:
    ans+=x*p
    x=x*(1.0-p)*(1.0-q)
print ans