If A = \[{{\left( -\text{ }1 \right)}^{1}}+{{\left( -\text{ }1 \right)}^{2}}+{{\left( -\text{ }1 \right)}^{3}}+\_\_\_\_\_\_+{{\left( -\text{ }1 \right)}^{1001}}\] and B = \[{{\left( -\text{ }1 \right)}^{1}}-{{\left( -\text{ }1 \right)}^{2}}+{{\left( -\text{ }1 \right)}^{3}}-{{\left( -\text{ }1 \right)}^{4}}+\_\_\_\_\_\_+{{\left( -\text{ }1 \right)}^{1001}},\text{ }\] then find A - B.

• A. -1002
• B.  1000
• C. -1001
• D.  1001
• E. None of these