5069: Duff in the Army
内存限制：256 MB
时间限制：2 S
标准输入输出
题目类型：传统
评测方式：文本比较
上传者：
提交：1
通过：1
题目描述
C. Duff in the Army
time limit per test
4 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output
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 ci. 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 p1,p2,...,px in increasing order.
If k=min(x,a), then Duff should tell Malek numbers k,p1,p2,...,pk 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.
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 ci. 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 p1,p2,...,px in increasing order.
If k=min(x,a), then Duff should tell Malek numbers k,p1,p2,...,pk 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.
Input
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 c1,c2,...,cm separated by spaces (1≤ci≤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).
Output
For each query, print numbers k,p1,p2,...,pk separated by spaces in one line.
Examples
Input
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
Output
1 3 2 2 3 0 3 1 2 4 1 2
Note
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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输出样例 复制