Problem C
Railway

CC-BY-SA-2.0, Bergen Railway Station, Kamil Porembiński via Wikimedia Commons

A couple of years ago the Bergen Ministry of Infrastructure prepared a plan for a new light railway network. This network was supposed to connect all $n$ neighbourhoods in the city with $n - 1$ railway tracks in such a way, that there would be a path from every neighbourhood to every other neighbourhood. The planned tracks are identified by numbers from $1$ to $n - 1$.

Years passed, new elections are approaching, and the railway network still exists only on paper. Therefore the Minister of Infrastructure (representing a party holding disagreement in high regard) decided to construct at least some part of the plan. He asked each of his $m$ deputy ministers to choose which neighbourhoods they thought should be connected. That will result in a list of necessary tracks for each deputy minister. If a deputy minister thinks that the neighbourhoods $a_1, \ldots , a_ s$ need to be connected, then according to him or her, the necessary tracks are all those which lie on planned paths from $a_ i$ to $a_ j$ for some $1 \leq i < j \leq s$.

The minister just received all lists from the deputy ministers. He decided to construct in the first place the tracks which are requested by at least $k$ deputy ministers. Your task is to prepare a list of these tracks.

Input

In the first line of the input there are three integers $n$, $m$ and $k$. The next $n - 1$ lines contain the plan; in the $i$-th of these lines there are two integers $a_ i$ and $b_ i$ ($1 \leq a_ i, b_ i \leq n, a_ i \neq b_ i$), specifying that the $i$-th track on the plan is between neighbourhoods $a_ i$ and $b_ i$.

In the next $m$ lines there are neighbourhoods chosen by deputy ministers; the $i$-th of these lines begins with an integer $s_ i$ which specify the number of neighbourhoods chosen by the $i$-th deputy minister. After it there are $s_ i$ integers specifying these neighbourhoods. The total length of all lists of deputy ministers is at most $S$, i.e. $\sum _{i=1}^{m}s_ i \leq S$.

We always have $2 \leq s_ i \leq n \leq 100\, 000$, $S \leq 150\, 000$, and $1 \leq k \leq m \leq 50\, 000$.

Output

In the first line of the output you should write one integer $r$, specifying the number of tracks which are requested by at least $k$ deputy ministers. In the second line you should write $r$ identifiers of these tracks in ascending order.

Explanation of sample

The first deputy minister thinks that tracks $1$–$3$, $2$–$3$, $3$–$4$ and $4$–$5$ are necessary. The second deputy minister considers tracks $3$–$4$ and $4$–$6$, and the third one only track $2$–$3$. Tracks $2$–$3$ and $3$–$4$ are necessary according to at least two deputy ministers.

6 3 2
1 3
2 3
3 4
6 4
4 5
4 1 3 2 5
2 6 3
2 3 2

2
2 3