410031: GYM103921 C Earthbending years

It is Earth Kingdom tradition to track the year with some piles of raised earth. To mark the new year, earthbenders come together to raise the ground $$$1$$$ unit, representing the new year.

Unfortunately, they can only raise the dirt from its initial height of $$$0$$$ to a maximum height of $$$3$$$ (since they lack proper training). As a solution, when a pile needs to be raised to a height of $$$4$$$, instead they gently lower the pile back to a height of $$$0$$$ and raise the area to the right by $$$1$$$ unit of height.

There are currently $$$N$$$ piles, representing the current year. Given the state of the dirt piles, determine what the piles would look like in $$$K$$$ years.

Two space-separated numbers, $$$1 \leq N \leq 1000$$$ and $$$1 \leq K \leq 10^4$$$.

The next $$$N$$$ numbers represent the current pile heights from left to right, where the last pile is guaranteed to have non-zero height.

The piles after $$$K$$$ years, from left to right, where the last pile has non-zero height.

3 6
3 2 2

1 0 3 

1 21
2

3 1 1