# Size of solutions in integer programming

Given a linear integer program $$Ax\leq b$$ with $$A\in\mathbb Z^{m\times n}$$ and $$b\in\mathbb Z^m$$ known is there a polynomial time algorithm to give tight upper bounds for $$\log_2\|x\|_\infty$$ and $$\log_2\|x\|_2$$ where $$x\in\mathbb Z^n$$ is unknown?