If $D = \begin{vmatrix} 1 & 1 & 1 \\ 1 & 1+x & 1 \\ 1 & 1 & 1+y \end{vmatrix}$ for $x \neq 0, y \neq 0$, then $D$ is :

Question

( A ) divisible by both $x$ and $y$
( B ) divisible by neither $x$ nor $y$
( C ) divisible by $x$ but not $y$
( D ) divisible by $x$ but not $y$