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 colors of these balls must form an increasing sequence.