Strange Transform

You are given an integer sequence $A_1, A_2, \ldots, A_N$. Let's define a transformation $f$. Applying $f$ on $A$ gives a new sequence $f(A) = [B_1, B_2, \ldots, B_N]$, where $B_N = A_N$ and $B_i = A_i \oplus A_{i+1}$ for each valid $i$. Next, let's denote the sequence obtained by starting with $A$ and applying the transformation $k$ times by $f^k(A)$. Formally, $f^0(A) = A$ and $f^{k+1}(A) = f(