The first and last elements are always equal to $$$1$$$.

There are at least $$$\lceil \frac{n - 1}{k} \rceil$$$ ones among the first $$$n - 1$$$ elements.

Try to solve the problem if all $$$a_i$$$ are equal.

After every operation, the last element of $$$b$$$ is equal to $$$0$$$.

If the last element of $$$a$$$ is $$$0$$$, then you can always achieve $$$b = a$$$ with some sequence of operations.

Try to solve the problem if $$$a$$$ consists of $$$k$$$ ones followed by single zero.

Consider the set of balls that were never moved by operations of type 2.

The relative order of these balls never changes, so their colors must form an increasing sequence.