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*<sub class="lower-index">*i*</sub>. 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*<sub class="lower-index">1</sub>, *p*<sub class="lower-index">2</sub>, ..., *p*<sub class="lower-index">*x*</sub> in increasing order. 

If *k* = *min*(*x*, *a*), then Duff should tell Malek numbers *k*, *p*<sub class="lower-index">1</sub>, *p*<sub class="lower-index">2</sub>, ..., *p*<sub class="lower-index">*k*</sub> 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.
The first line of input contains three integers, *n*, *m* and *q* (1 ≤ *n*, *m*, *q* ≤ 10<sup class="upper-index">5</sup>).

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*<sub class="lower-index">1</sub>, *c*<sub class="lower-index">2</sub>, ..., *c*<sub class="lower-index">*m*</sub> separated by spaces (1 ≤ *c*<sub class="lower-index">*i*</sub> ≤ *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).
print("_RANDOM_GUESS_1690486209.0252557")# 1690486209.0252757