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:
a,b,c,d = map(float,raw_input().split())
ans = a/b
tmp = (b-a)/b
kid = ((tmp)*(d-c)/d)*a/b
#print kid
for _ in xrange(10000):
    ans+=kid#/(10**_)
    kid = ((kid/a*(b-a))*(d-c)/d)*a/b
    #tmp = ((tmp)*c/d)*(-a)/b
print ans