What is the result of $1\div 1\frac{2}{2001}\div 1\frac{2}{2003}\cdots \div 1\frac{2}{2023}$? 
选项为:A:$$1$$  B:$\frac{2025}{2001}$  C:$\frac{2021}{2025}$  D:$\frac{2001}{2025}$  E:$\frac{1}{2001}$  请回答其中一个选项.