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C. Duff in the Army

time limit per test

4 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard 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 *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.

Input

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).

Output

For each query, print numbers *k*, *p*_{1}, *p*_{2}, ..., *p*_{k} 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):

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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