Binary counter amortized analysis This is a question I have stumbled upon in my textbook, and didn't really know how to approach:

Given a $k$-bit binary counter.
We have an operation Increment, which adds 1 to the counter.
We add a new operation Decrement, which subtracts 1 from the counter.
Prove that the cost for executing $n$ operations is $\Theta(nk)$.
Hint: Think of a value $n$ such that the transition from $n$ to $n+1$ and back is very costly.