A regular octahedron is formed by joining the centers of adjoining faces of a cube. What is the ratio of the volume of the octahedron to the volume of the cube? The original answer is in the form \(\frac{k}{m}\), where \(\frac{k}{m}\) is a simplified fraction. Please provide the value of k + m.

Let's think step by step and output the final answer within \boxed{}.
user