Coloring Practice (Small)

You paint the vertices of a regular $n$-gon with $k$ colors. You do not have to use every color.

Two paintings count as one and the same case when a finite number of the following operations turns one into the other.

• Rotate the polygon.
• Flip the polygon over.
• Pick two different colors $X$ and $Y$, repaint every vertex of color $X$ with color $Y$, and repaint every vertex of color $Y$ with color $X$. It is allowed that no vertex has color $X$ or color $Y$.

Count how many different paintings there are.

The first line contains $n$ and $k$, separated by a space.

$3 \le n \le 6$, $1 \le k \le 5$

Print the number of different paintings that satisfy the conditions, modulo 1,000,000,007, on one line.