Rings and Groups
Statement
In algebra, a GROUP is a set in which you can perform one operation (for this problem, either addition or multiplication mod N) on any two members of the set, and the result is also in the set. There is also an identity requirement, so additive groups must contain a 0, and multiplicative groups a 1.
A RING is a group under both addition and multiplication.
Classify each set as a GROUP+, GROUP*, RING, or NONE.
Input description
<<Line 1:>> The modulus [[N]]
<<Line 2:>> The [[SetSize]]
<<Line 3:>> Space-separated integer values that make up the set
Output description
One line classifying the set.
Constraints
[[N]] ≤ 50
[[SetSize]] ≤ 50
0≤ set values ≤ 50
Game modes
Fastest
Test cases
Test 1 Test
Input
12
6
0 2 4 6 8 10
Output
GROUP+
Validator 1 Validator
Input
7
6
1 2 3 4 5 6
Output
GROUP*
Test 2 Test
Input
11
10
1 2 3 4 5 6 7 8 9 10
Output
GROUP*
Validator 2 Validator
Input
22
11
0 2 4 6 8 10 12 14 16 18 20
Output
GROUP+
Test 3 Test
Input
35
32
0 1 2 4 5 6 7 8 9 10 11 12 13 14 15 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 33 34
Output
NONE
Validator 3 Validator
Input
35
32
0 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 22 23 24 25 26 27 29 30 31 32 33 34
Output
NONE
Test 4 Test
Input
25
25
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Output
RING
Validator 4 Validator
Input
30
30
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
Output
RING
Test 5 Test
Input
50
49
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49
Output
NONE
Validator 5 Validator
Input
50
49
0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49
Output
NONE
Solution language
Solution
Stub generator input