I think the question is DCFL
We can design the satck like normal DCFL for amdl(as m=l it would be like a^nb^n)
and for bn+k we can design a stack like for one input it will insert a value let 'X' in stack and encountering a b again it will pop 'X' So when the stack iscontained the last value inserted at the time of am then it is understandable that n+k=even
So we can transit to a next state when stackhas new one value in the second state i.e ODD
so all moves are obvious and only one transition is possible for each case
it is DCFL but not regular
correction required , I am not 100%sure