A cascade system having the impulse response \({{\rm{h}}_1}\left( {\rm{n}} \right) = \left\{ {\begin{array}{*{20}{l}}{1, - 1}\\\uparrow\end{array}} \right\}\) and \({{\rm{h}}_2}\left( {\rm{n}} \right) = \left\{ {\begin{array}{*{20}{l}}{1,{\rm{\;}}1}\\\uparrow\end{array}} \right\}\) is shown in the figure below, where symbol ↑ denotes the time origin.The input sequence x(n) for which the cascade system produces an output sequence \({\rm{y}}\left( {\rm{n}} \right) = \left\{ {\begin{array}{*{20}{l}}{1,{\rm{\;}}2,{\rm{\;}}1,{\rm{\;}} - 1,{\rm{\;}} - 2,{\rm{\;}} - 1}\\\uparrow\end{array}} \right\}\) is

• A. \({\rm{x}}\left( {\rm{n}} \right) = \left\{ {\begin{array}{*{20}{l}}{1,{\rm{\;}}2,{\rm{\;}}1,{\rm{\;}}1}\\\uparrow\end{array}} \right\}\)
• B. \({\rm{x}}\left( {\rm{n}} \right) = \left\{ {\begin{array}{*{20}{l}}{1,{\rm{\;}}1,{\rm{\;}}2,{\rm{\;}}2}\\\uparrow\end{array}} \right\}\)
• C. \({\rm{x}}\left( {\rm{n}} \right) = \left\{ {\begin{array}{*{20}{l}}{1,{\rm{\;}}1,{\rm{\;}}1,{\rm{\;}}1}\\\uparrow\end{array}} \right\}\)
• D. \({\rm{x}}\left( {\rm{n}} \right) = \left\{ {\begin{array}{*{20}{l}}{1,{\rm{\;}}2,{\rm{\;}}2,{\rm{\;}}1}\\\uparrow\end{array}} \right\}\)