Is a divisibility language context free? I am working to see if this language would be context free:

L = { 0n1k : n/k is an integer }

After playing with it for a little while, I believe that the language is not context free. Now I am looking to use the pumping lemma to prove that it is not, but am struggling a bit to apply it to this language, which is making me question whether it might be a CFL.
Is this language context free? If not, how should I approach using the pumping lemma to prove that it is not.

Let $p$ be the pumping length and pick $k>p$.
As $0^k1^k\in L$, we can write $0^k1^k=xyz$ with $|xy|\le p$, $|y|\ge 1$, and $xy^iz\in L$ for all $i\ge 0$. We conclude that $x=0^r, y=0^s$ wirh $r\ge0$, $s\ge 1$. Then $xy^0z=0^{k-s}1^k\notin L$.
