Ouroboros

You are given a cyclic array $A$ of size $N$ and an integer step size $K$.

Transform the array such that every element $A_i$ becomes the sum of its original value and the value of the element $K$ steps ahead in the cycle.

Formally, update every element as follows: $A'$i = A_i + A{(i+K) \pmod N}

Note: This transformation must be performed in-place with $O(1)$ auxiliary space. The calculation for $A'_i$ must use the values of $A$ before any updates were made.