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Case 1:
6 4
10 3 4 2

OPT(4): 1+2+3+4
OPT(4): 1+4+5, 3

Same as in problem description
---------------------------
Case 2:
6 5
10 2 4 5 3

OPT(6): 1+3+6, 2, 4, 5, 3
OPT(6): 4+6, 2, 1+3, 5

Shut the Box!
Same as in problem description
---------------------------
Case 3:
10 10
1 1 3 4 5 6 7 8 9 10

OPT(1): 1

Game ends on the second turn, as no 1 available
---------------------------
Case 4:
22 22
22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

OPT(22): straightforward

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Case 5:
6 5
10 1 6 4 5

OPT(6): 2+3+5, 1, 6, 4

Same as previous but with extraneous unused turn
---------------------------
Case 6:
5 5
1 2 3 4 5

OPT(5): 1, 2, 3, 4, 5

Plain and simple
---------------------------
Case 7:
5 5
5 4 3 2 1

OPT(5): 5, 4, 3, 2, 1

Plain and simple, reversed
---------------------------
Case 8:
5 5
3 3 3 3 3

OPT(3): 1+2, 3  and then stuck (or 3, 1+2)

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Case 9:
6 1
1

OPT(1): 1

Must handle small case without error
---------------------------
Case 10:
10 1
21

OPT(6): 1+2+3+4+5+6

Must find best way to use a single value and noting that single value
is allowed to be significantly bigger than N.

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Case 11:
10 2
20 1

OPT(6): 2+3+4+5+6, 1

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Case 12:
6 5
4 6 1 1 5

OPT(4): 1+3, 2+4
OPT(4): 4, 1+2+3
(but not 4, 6, 1)

Key is that it is better to get stuck after two turns, than take a
different approach that uses three turns (but fewer marks). Note that
there is no way to use the 5 in any scenario.

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Case 13:
7 6
3 7 5 1 7 6

OPT(5): 1+2, 3+4, 5
OPT(5): 3, 2+5, 1+4
(but not 3, 7, 5, 1)

As with previous case, better to get stuck earlier but get more marks,
and no way to use the 6 in any scenario.

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Case 14:
12 3
12 11 10
OPT(7): 1+2+3+6, 4+7, 10  (among other solutions)

Testing some multimark combinations
---------------------------
Case 15:
15 3
15 14 13
OPT(8): 1+2+3+4+5, 6+8, 13  (among other solutions)

Testing some multimark combinations
---------------------------
Case 16:
18 3
18 17 16
OPT(9): 3+4+5+6, 2+7+8, 1+15  (among other solutions)

Testing some multimark combinations
---------------------------
Case 17:
21 3
21 20 19
OPT(10): 1+2+5+6+7, 3+8+9, 4+15  (among other solutions)

Testing some multimark combinations
---------------------------
Case 18:
22 4
22 22 22 22

OPT(12): 2+3+4+6+7, 5+8+9, 1+10+11, 22

Testing more multi combinations
---------------------------
Case 19:
6 4
10 1 6 4

OPT(6): 2+3+5, 1, 6, 4

Shut the Box!
---------------------------
Case 20:

22 8
22 21 22 21 22 21 22 21

OPT(18): 3+6+13, 10+11, 8+14, 9+12, 7+15, 1+4+16, 5+17, 2+19

Lots of repetition to thwart brute force, but not all the same.

---------------------------
Case 21:
22 10
22 22 22 22 22 22 22 22 22 22

OPT(20):  1+10+11, 9+13, 8+14, 7+15, 6+16, 5+17, 4+18, 3+19, 2+20, 22

This is a case in which dynamic programming does quite quickly, but a
brute force approach will take too long.  Optimal is any combination
of turns 1+20, 2+19, 3+18, 4+17, ... for a total of 20 marks.
---------------------------