C. Duff in the Army

хугацааны хязгаарлалт 4 секунд

санах ойн хязгаарлалт 512 мегабайт

оролт стандарт оролт

гаралт стандарт гаралт

Recently Duff has been a soldier in the army. Malek is her commander.

Their country, Andarz Gu has $n$ cities (numbered from $1$ to $n$) and $n - 1$ bidirectional roads. Each road connects two different cities. There exist a unique path between any two cities.

There are also $m$ people living in Andarz Gu (numbered from $1$ to $m$). Each person has and ID number. ID number of $i - th$ person is $i$ and he/she lives in city number $c_{i}$. Note that there may be more than one person in a city, also there may be no people living in the city.

Malek loves to order. That's why he asks Duff to answer to $q$ queries. In each query, he gives her numbers $v, u$ and $a$.

To answer a query:

Assume there are $x$ people living in the cities lying on the path from city $v$ to city $u$. Assume these people's IDs are $p_{1}, p_{2}, ..., p_{x}$ in increasing order.

If $k = min(x, a)$, then Duff should tell Malek numbers $k, p_{1}, p_{2}, ..., p_{k}$ in this order. In the other words, Malek wants to know $a$ minimums on that path (or less, if there are less than $a$ people).

Duff is very busy at the moment, so she asked you to help her and answer the queries.


The first line of input contains three integers, $n, m$ and $q$ ($1 ≤ n, m, q ≤ 10^{5}$).

The next $n - 1$ lines contain the roads. Each line contains two integers $v$ and $u$, endpoints of a road ($1 ≤ v, u ≤ n$, $v ≠ u$).

Next line contains $m$ integers $c_{1}, c_{2}, ..., c_{m}$ separated by spaces ($1 ≤ c_{i} ≤ n$ for each $1 ≤ i ≤ m$).

Next $q$ lines contain the queries. Each of them contains three integers, $v, u$ and $a$ ($1 ≤ v, u ≤ n$ and $1 ≤ a ≤ 10$).


For each query, print numbers $k, p_{1}, p_{2}, ..., p_{k}$ separated by spaces in one line.

Орчуулсан: [орчуулагдаж байгаа]

Жишээ тэстүүд

5 4 5
1 3
1 2
1 4
4 5
2 1 4 3
4 5 6
1 5 2
5 5 10
2 3 3
5 3 1
1 3
2 2 3
3 1 2 4
1 2


Graph of Andarz Gu in the sample case is as follows (ID of people in each city are written next to them):

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