Consider the "twisted" variant of Reed$-$Solomon code that maps a message polynomial $m(x)=m_0+m_{1}x+$cdots$+m_{l-1}{x}^{l-1}$ to the evaluations of the polynomial $x*m(x)$ on the sequence $,$ where $l=n-k.$ Prove that this code equals the dual of the above Reed$-$Solomon code.