Question 130
Let $m$, $n$ be integers with $4 \lt m \lt n$, and $A_1, A_2, \dots, A_{2n+1}$ be a regular $2n + 1$ polygon. In addition, let $P = \{A_1, A_2, \dots, A_{2n+1}\}$. Find the number of convex $m$-gons with exactly two acute internal angles whose vertices are all in $P$. (Posed by Leng Gangsong)