The following shows a tree with 1023 vertices, where consecutive natural numbers from 1 to 1023 are assigned to each vertex according to a rule. Let $M(a, b)$ be the maximum natural number corresponding to a vertex that is commonly included in both the path from the vertex corresponding to 1 to the vertex corresponding to $a$ and the path from the vertex corresponding to 1 to the vertex corresponding to $b$. For example, $M(4, 11) = 2$ and $M(7, 12) = 3$. If $M(33, 79) = k$, find the value of $10k$. [4 points]
The following shows a tree with 1023 vertices, where consecutive natural numbers from 1 to 1023 are assigned to each vertex according to a rule.
Let $M(a, b)$ be the maximum natural number corresponding to a vertex that is commonly included in both the path from the vertex corresponding to 1 to the vertex corresponding to $a$ and the path from the vertex corresponding to 1 to the vertex corresponding to $b$.
For example, $M(4, 11) = 2$ and $M(7, 12) = 3$.
If $M(33, 79) = k$, find the value of $10k$. [4 points]