I've solved this problem and got WA after rejudge.
And I have one question: does the word "lexicographic" mean it's usual meaning for sets (e.g. set A lexicographically smaller than set B if there exists some i that i-th element is in A, but no in B, and for all j < i j-th element is both in A and B). Or it means something else?

Yes, "lexicographic" has its usual meaning.

in
12 3
.... 12 linearly independent vectors
1
1
...
1
1


out
3
1
10
11

Yes?

Firstly, there are no linearly independent vectors 12 in three-dimensinal. :-)
Secondly, I think right answer is
3
1
2
3