A9977 | Duff in the Army

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.