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

$\begin{array}{1 1}(a)\;divisible\;by\;x\;but\;not\;y\\(b)\;divisible\;by\;y\;but\;not\;x\\(c)\;divisible\;by\;neither\;x\;nor\;y\\(d)\;divisible\;by\;both\;x\;and\;y\end{array}$