#[Pyth](https://github.com/isaacg1/pyth), 120 - 20 - 15 = 85

    Jm]dUzL[-bQ+bQ?tb%bQb?hb%hbQb)FNJIgNQB~Jm+NkyeN;KS{msm+@zd@S*Q<GQxsbdUzfqSsTUz^fqsmv@*QzkY/smvbzQJQ|jb<K/lKu*GhHUQ1"None

Notes:

* Saved 10 characters by switching to newline separated input.

Test run:

    pyth programs/sum_group.pyth <<< '156790809
    3'
    1a5a6b7c9a0b8c0c9b
        
    pyth programs/sum_group.pyth <<< '156790808
    3'
    None
    
    pyth programs/sum_group.pyth <<< '1221
    2'
    1a2a2b1b
    1a2b2a1b
    
    pyth programs/sum_group.pyth <<< '1221 2'
    1a2a2b1b
    1a2b2a1b

Explanation to follow.