Some rumors about Zhang3 have been spread on the Internet. Zhang3 needs to dispel the rumors, but she's busy preparing her birthday party, so she asks her $m$ classmates for help. Her classmates decide to have a meeting for discussion.
The $m$ classmates live in the same community. There are $n$ houses in the community, labeled $1, 2, \ldots, n$. There are $(n - 1)$ roads connecting the houses, the $i^\mathrm{th}$ of which connects house $(i + 1)$ and $f_{i + 1}$, forming a tree. Each road is 1 km long.
The $m$ classmates live in $m$ different houses. They always choose such a house to have the meeting, that the total distance to travel for the $m$ classmates is minimized. The optimal total distance (in km) to travel is called the cost of the meeting.
Zhang3 doesn't know which houses her classmates live in, so there are $\binom{n}{m}$ different cases of that. Zhang3 wants to know the sum of the cost in all cases. As the answer can be very large, please help her calculate the answer modulo $10^9 + 7$.