How to build query: Should have those values and must have something else?

it is easy to create a boolean should query. But my problem is that I need documents which contains those terms I've specified in the query and must contain something else.
For example a document has a field "test":"a1 a2", and another document has "test":"a1 a2 a3".
When I run my should query with terms "a1" and "a2" I'm getting both documents, which is expected. But I need to omit somehow the documents which contains only those terms (the first one in this example). And I need only the documents which contain more than those provided terms.
Is it possible?
Any ideas are appreciated.

Thank you,

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