C. Duff in the Armytime limit per test4 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputRecently 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.InputThe 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).OutputFor each query, print numbers k, p1, p2, ..., pk separated by spaces in one line.ExamplesInput5 4 51 31 21 44 52 1 4 34 5 61 5 25 5 102 3 35 3 1Output1 32 2 303 1 2 41 2NoteGraph of Andarz Gu in the sample case is as follows (ID of people in each city are written next to them):  
Input5 4 51 31 21 44 52 1 4 34 5 61 5 25 5 102 3 35 3 1
Output1 32 2 303 1 2 41 2
['data structures', 'trees', '*2200']