Rudolf and Snowflakes (simple version)

This is a simple version of the problem. The only difference is that in this version $$$n \le 10^6$$$.

One winter morning, Rudolf was looking thoughtfully out the window, watching the falling snowflakes. He quickly noticed a certain symmetry in the configuration of the snowflakes. And like a true mathematician, Rudolf came up with a mathematical model of a snowflake.

He defined a snowflake as an undirected graph constructed according to the following rules:

• Initially, the graph has only one vertex.
• Then, more vertices are added to the graph. The initial vertex is connected by edges to $$$k$$$ new vertices ($$$k > 1$$$).
• Each vertex that is connected to only one other vertex is connected by edges to $$$k$$$ more new vertices. This step should be done at least once.

The smallest possible snowflake for $$$k = 4$$$ is shown in the figure.

After some mathematical research, Rudolf realized that such snowflakes may not have any number of vertices. Help Rudolf check if a snowflake with $$$n$$$ vertices can exist.