Let $$A = \left\{(x,y) \in \mathbb{R}^2 : y \geq 0, 2x \leq y \leq \sqrt{4-(x-1)^2}\right\}$$ and
$$B = \left\{(x,y) \in \mathbb{R} \times \mathbb{R} : 0 \leq y \leq \min\left\{2x, \sqrt{4-(x-1)^2}\right\}\right\}$$. Then the ratio of the area of $$A$$ to the area of $$B$$ is

A

$$\frac{\pi-1}{\pi+1}$$

B

$$\frac{\pi}{\pi-1}$$

C

$$\frac{\pi}{\pi+1}$$

D

$$\frac{\pi+1}{\pi-1}$$