Space complexity of integer programming

Given $A\in\Bbb Z^{n\times k}$, $v\in\Bbb Z^n$ and variables $x_1,\dots,x_k$ given as a vector $x$ we know that solving $x\in\Bbb Z^k$ in $Ax\leq v$ is fixed parameter tractable. There is a deterministic algorithm that runs in $O((nk)^{ck})$ time for some $c>0$. What is the space complexity of the algorithm? Does it run in polynomial space?