For non-negative integers $m$, $n$ define a function as follows

$$f(m,n) = \begin{cases} n+1 & \text{ if } m=0 \\ f(m-1, 1) & \text{ if } m \neq 0, n=0 \\ f(m-1, f(m,n-1)) & \text{ if } m \neq 0, n \neq 0 \end{cases}$$ Then the value of $f(1,1)$ is

B is the correct answer.