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