Problem C: Divisibility
Consider an arbitrary sequence of integers. One can place + or - operators between
integers in the sequence, thus deriving different arithmetical expressions
that evaluate to different values. Let us, for example, take the sequence:
17, 5, -21, 15. There are eight possible expressions:
| 17 | + | 5 | + | -21 | + | 15 | = | 16
|
| 17 | + | 5 | + | -21 | - | 15 | = | -14
|
| 17 | + | 5 | - | -21 | + | 15 | = | 58
|
| 17 | + | 5 | - | -21 | - | 15 | = | 28
|
| 17 | - | 5 | + | -21 | + | 15 | = | 6
|
| 17 | - | 5 | + | -21 | - | 15 | = | -24
|
| 17 | - | 5 | - | -21 | + | 15 | = | 48
|
| 17 | - | 5 | - | -21 | - | 15 | = | 18
|
We call the sequence of integers divisible by K if
+ or - operators can be placed between integers in the sequence in such
way that resulting value is divisible by K. In the above example,
the sequence is divisible by 7 (17+5+-21-15=-14) but is not divisible by 5.
You are to write a program that will determine divisibility of
sequence of integers.
Input
The first line of the input file contains a integer M indicating the number of
cases to be analyzed. Then M couples of lines follow.
For each one of this couples,
the first line contains two integers, N
and K (1 <= N <= 10000, 2 <= K <= 100)
separated by a space.
The second line contains a sequence of N integers separated
by spaces. Each integer is not greater than 10000 by it's absolute
value.
Output
For each case in the input file, write to the output file the word "Divisible" if given sequence of integers is
divisible by K or "Not divisible" if it's not.
Sample input
2
4 7
17 5 -21 15
4 5
17 5 -21 15
Sample Output
Divisible
Not divisible