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