CF587C.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.

最近，达芙（Duff）成为了一名士兵，马莱克（Malek）是她的指挥官。

她们的祖国安达尔兹古（Andarz Gu）共有 $n$ 座城市（编号从 $1$ 到 $n$）以及 $n-1$ 条双向道路。每条道路连接两个不同的城市，且任意两座城市之间都存在唯一的一条路径。

安达尔兹古还有 $m$ 位居民（编号从 $1$ 到 $m$），每人有一个唯一的 ID 号；第 $i$ 位居民的 ID 号为 $i$，居住在城市 $c_i$。注意：一座城市中可能有多人居住，也可能无人居住。

马莱克酷爱发号施令，因此他要求达芙回答 $q$ 个查询。每个查询给出三个数 $v$、$u$ 和 $a$。

对于每个查询，回答方式如下：

设位于城市 $v$ 到城市 $u$ 的路径上的所有城市中居住的人数为 $x$；将这些人的 ID 按升序排列为 $p_1, p_2, \dots, p_x$。

令 $k = \min(x, a)$，则达芙需向马莱克依次报告 $k, p_1, p_2, \dots, p_k$。换言之，马莱克希望知道该路径上 ID 最小的 $a$ 个人（若人数不足 $a$，则报告全部）。

达芙此刻非常忙碌，因此她请你帮忙回答这些查询。

The first line of input contains three integers, n, m and q (1 ≤ n, m, q ≤ 105).

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).

输入的第一行包含三个整数 $n$、$m$ 和 $q$（$1 \le n, m, q \le 10^5$）。

接下来的 $n - 1$ 行描述道路。每行包含两个整数 $v$ 和 $u$，表示一条道路的两个端点（$1 \le v, u \le n$，且 $v \ne u$）。

下一行包含 $m$ 个整数 $c_1, c_2, ..., c_m$，以空格分隔（对每个 $1 \le i \le m$，满足 $1 \le c_i \le n$）。

接下来的 $q$ 行为查询。每行包含三个整数 $v$、$u$ 和 $a$（$1 \le v, u \le n$，且 $1 \le a \le 10$）。

For each query, print numbers k, _p_1, _p_2, ..., p__k separated by spaces in one line.

对于每个查询，在一行中输出数字 $k$、$p_1$、$p_2$、…、$p_k$，以空格分隔。

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

样例中的安达尔兹·古图的图如下所示（每个城市中人员的编号写在其旁边）：