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.

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.

Note

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