Continued Fraction of a Rational Number The continued fraction of a number n is a fraction of the following form:

which converges to n.

The sequence a in a continued fraction is typically written as: [a0; a1, a2, a3, ..., an].

Your goal is to return the continued fraction of the given rational number (positive or negative), whether it is an:


integer x
fraction x/y
decimal x.yz


Input

May be a string representation, or numbers. For fractions, it may be a string, or some native data type for handling fractions, but you may not take it as a decimal.

Output 

May be a delimited list or string of the convergents (the resulting numbers). The output does not have to have a semi-colon between a0 and a1, and may use a comma instead.

Note that although [3; 4, 12, 4] and [3; 4, 12, 3, 1] are both correct, only the first will be accepted, because it is simpler.

Examples:

860438      [860438]
3.245       [3; 4, 12, 4]
-4.2        [-5; 1, 4]
-114.7802   [-115; 4, 1, 1, 4, 1, 1, 5, 1, 1, 4]
0/11        [0]
1/42        [0; 42]
2/7         [0; 3, 2]
-18/17056   [-1; 1, 946, 1, 1, 4]
-17056/18   [-948; 2, 4]


Rules


Shortest code wins.
Built-ins are allowed, but I'd also like you to post in the same answer what it would be without built-ins, so that you have to know how to do it.
Ruby, 45 43 46 bytes

f=-&gt;n{x,y=n.to_r.divmod 1;[x,*y==0?[]:f[1/y]]}


Accepts input as a string.

All test cases pass:

llama@llama:~$ for n in 860438 3.245 -4.2 -114.7802 0/11 1/42 2/7 -18/17056 -17056/18; do ruby -e 'f=-&gt;n{x,y=n.to_r.divmod 1;[x,*y==0?[]:f[1/y]]}; p f["'$n'"]'; done
[860438]
[3, 4, 12, 4]
[-5, 1, 4]
[-115, 4, 1, 1, 4, 1, 1, 5, 1, 1, 4]
[0]
[0, 42]
[0, 3, 2]
[-1, 1, 946, 1, 1, 4]
[-948, 2, 4]


Thanks to Kevin Lau for 2 bytes!