## Introduction
A decimal is terminating if it has a finite number of decimal digits. For example, 0.4 (2/5) is terminating because it has one decimal digit.
A decimal is purely periodic if it has an infinite number of decimal digits and has no decimal digits before its repetent (the part of the decimal that repeats.) For example, 0.142857142857142… (1/7) is purely periodic because it has a repetend 142857, which starts repeating immediately after the decimal point.
A decimal is eventually periodic if it has an infinite number of decimal digits and has a finite number of decimal digits before its repetent (the part of the decimal that repeats.) For example, 0.166666666666666… (1/6) is eventually periodic because its repetend 6 starts repeating after a 1.
## Your task
Write a program or function that, when given a fraction in the form *p*/*q* (integers, 0 <= *p* < *q* <= 100) will determine if its decimal representation is terminating, purely periodic, or eventually periodic.
## Test cases
0/1 => Terminating
0/2 => Terminating
1/2 => Terminating
0/3 => Terminating
1/3 => Purely Periodic
2/3 => Purely Periodic
0/4 => Terminating
1/4 => Terminating
2/4 => Terminating
3/4 => Terminating
0/5 => Terminating
1/5 => Terminating
2/5 => Terminating
3/5 => Terminating
4/5 => Terminating
0/6 => Terminating
1/6 => Eventually Periodic
2/6 => Purely Periodic
3/6 => Terminating
4/6 => Purely Periodic
5/6 => Eventually Periodic
0/7 => Terminating
1/7 => Purely Periodic
2/7 => Purely Periodic
3/7 => Purely Periodic
4/7 => Purely Periodic
5/7 => Purely Periodic
6/7 => Purely Periodic
0/8 => Terminating
1/8 => Terminating
2/8 => Terminating
3/8 => Terminating
4/8 => Terminating
5/8 => Terminating
6/8 => Terminating
7/8 => Terminating
0/9 => Terminating
1/9 => Purely Periodic
2/9 => Purely Periodic
3/9 => Purely Periodic
4/9 => Purely Periodic
5/9 => Purely Periodic
6/9 => Purely Periodic
7/9 => Purely Periodic
8/9 => Purely Periodic
0/10 => Terminating
1/10 => Terminating
2/10 => Terminating
3/10 => Terminating
4/10 => Terminating
5/10 => Terminating
6/10 => Terminating
7/10 => Terminating
8/10 => Terminating
9/10 => Terminating
0/11 => Terminating
1/11 => Purely Periodic
2/11 => Purely Periodic
3/11 => Purely Periodic
4/11 => Purely Periodic
5/11 => Purely Periodic
6/11 => Purely Periodic
7/11 => Purely Periodic
8/11 => Purely Periodic
9/11 => Purely Periodic
10/11 => Purely Periodic
0/12 => Terminating
1/12 => Eventually Periodic
2/12 => Eventually Periodic
3/12 => Terminating
4/12 => Purely Periodic
5/12 => Eventually Periodic
6/12 => Terminating
7/12 => Eventually Periodic
8/12 => Purely Periodic
9/12 => Terminating
10/12 => Eventually Periodic
11/12 => Eventually Periodic
0/13 => Terminating
1/13 => Purely Periodic
2/13 => Purely Periodic
3/13 => Purely Periodic
4/13 => Purely Periodic
5/13 => Purely Periodic
6/13 => Purely Periodic
7/13 => Purely Periodic
8/13 => Purely Periodic
9/13 => Purely Periodic
10/13 => Purely Periodic
11/13 => Purely Periodic
12/13 => Purely Periodic
0/14 => Terminating
1/14 => Eventually Periodic
2/14 => Purely Periodic
3/14 => Eventually Periodic
4/14 => Purely Periodic
5/14 => Eventually Periodic
6/14 => Purely Periodic
7/14 => Terminating
8/14 => Purely Periodic
9/14 => Eventually Periodic
10/14 => Purely Periodic
11/14 => Eventually Periodic
12/14 => Purely Periodic
13/14 => Eventually Periodic
0/15 => Terminating
1/15 => Eventually Periodic
2/15 => Eventually Periodic
3/15 => Terminating
4/15 => Eventually Periodic
5/15 => Purely Periodic
6/15 => Terminating
7/15 => Eventually Periodic
8/15 => Eventually Periodic
9/15 => Terminating
10/15 => Purely Periodic
11/15 => Eventually Periodic
12/15 => Terminating
13/15 => Eventually Periodic
14/15 => Eventually Periodic
0/16 => Terminating
1/16 => Terminating
2/16 => Terminating
3/16 => Terminating
4/16 => Terminating
5/16 => Terminating
6/16 => Terminating
7/16 => Terminating
8/16 => Terminating
9/16 => Terminating
10/16 => Terminating
11/16 => Terminating
12/16 => Terminating
13/16 => Terminating
14/16 => Terminating
15/16 => Terminating
0/17 => Terminating
1/17 => Purely Periodic
2/17 => Purely Periodic
3/17 => Purely Periodic
4/17 => Purely Periodic
5/17 => Purely Periodic
6/17 => Purely Periodic
7/17 => Purely Periodic
8/17 => Purely Periodic
9/17 => Purely Periodic
10/17 => Purely Periodic
11/17 => Purely Periodic
12/17 => Purely Periodic
13/17 => Purely Periodic
14/17 => Purely Periodic
15/17 => Purely Periodic
16/17 => Purely Periodic
0/18 => Terminating
1/18 => Eventually Periodic
2/18 => Purely Periodic
3/18 => Eventually Periodic
4/18 => Purely Periodic
5/18 => Eventually Periodic
6/18 => Purely Periodic
7/18 => Eventually Periodic
8/18 => Purely Periodic
9/18 => Terminating
10/18 => Purely Periodic
11/18 => Eventually Periodic
12/18 => Purely Periodic
13/18 => Eventually Periodic
14/18 => Purely Periodic
15/18 => Eventually Periodic
16/18 => Purely Periodic
17/18 => Eventually Periodic
0/19 => Terminating
1/19 => Purely Periodic
2/19 => Purely Periodic
3/19 => Purely Periodic
4/19 => Purely Periodic
5/19 => Purely Periodic
6/19 => Purely Periodic
7/19 => Purely Periodic
8/19 => Purely Periodic
9/19 => Purely Periodic
10/19 => Purely Periodic
11/19 => Purely Periodic
12/19 => Purely Periodic
13/19 => Purely Periodic
14/19 => Purely Periodic
15/19 => Purely Periodic
16/19 => Purely Periodic
17/19 => Purely Periodic
18/19 => Purely Periodic
0/20 => Terminating
1/20 => Terminating
2/20 => Terminating
3/20 => Terminating
4/20 => Terminating
5/20 => Terminating
6/20 => Terminating
7/20 => Terminating
8/20 => Terminating
9/20 => Terminating
10/20 => Terminating
11/20 => Terminating
12/20 => Terminating
13/20 => Terminating
14/20 => Terminating
15/20 => Terminating
16/20 => Terminating
17/20 => Terminating
18/20 => Terminating
19/20 => Terminating
<sub>You can find all test cases [here](http://pastebin.com/raw/We01u4eF).</sub>
You are allowed to choose your own 3 values for the output, but it must be clear as to which one it is.
Remember, this is [tag:code-golf], so the code with the smallest number of bytes wins.