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.

$\text{[math]}$

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, ..., p_x in increasing order.

If k = min(x, a), then Duff should tell Malek numbers k, p₁, p₂, ..., 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.

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, ..., 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).

Output

For each query, print numbers k, p₁, p₂, ..., p_k separated by spaces in one line.

Note

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

$\text{[math]}$

Duff in the Army

Examples