If $\begin{vmatrix}x & x^2 & 1+px^3\\y & y^2 & 1+py^3\\z & z^2 & 1+pz^3\end{vmatrix}=\lambda (x-y) (y-z) (z-x), $ then value of $\lambda $ is :

$pxyz$ 0 $1+pxyz$ $1-pxyz$

$1+pxyz$