keys with multiple values

I have two files, A, B, with the following structure:

The key is $2.  The value of the key is the rest of the record.
So keys can have multiple values.  Disregard duplicate key-value pairs,
i.e. consider unique lines only.  I need to print out all key-value
pairs that belong to one file, but not to the other.  So I need something li
ke
this.
___________________
key    A       B
===   ===     ===
k1    A_11    B_11
A_21    B_21
B_31

k2    A_12
A_22

k3            B_13

...
____________________
For any fixed n,
A_pn != A_qn if p != q
B_pn != B_qn if p != q
A_pn != B_qn for all p, q

--
Regards,

---Robert