If $$f(x, y) = x^n . y^n$$ and $$f\left(4x, \frac{y}{2}\right) = k.f(x, y)$$ then k =

A

$$4n - \frac{m}{2}$$

B

$$2(n - m)$$

C

$$2^{2n - m}$$

D

$$2^{m - 2n}$$