2015 AMC 12B Problem 20

For every positive integer n, let \text{mod}_5 (n) be the remainder obtained when n is divided by 5. Define a function f: \{0,1,2,3,\ldots\} \times \{0,1,2,3,4\} \to \{0,1,2,3,4\} recursively as follows:

f(i,j) = \begin{cases}\text{mod}_5 (j+1) & \text{ if } i = 0 \text{ and } 0 \le j \le 4 \text{,}\\ f(i-1,1) & \text{ if } i \ge 1 \text{ and } j = 0 \text{, and} \\ f(i-1, f(i,j-1)) & \text{ if } i \ge 1 \text{ and } 1 \le j \le 4. \end{cases}

What is f(2015,2)?

\textbf{(A)}\; 0 \qquad\textbf{(B)}\; 1 \qquad\textbf{(C)}\; 2 \qquad\textbf{(D)}\; 3 \qquad\textbf{(E)}\; 4

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.