CF587C Duff in the Army

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.

The first line of input contains three integers, $ n,m $ and $ q $ ( $ 1

For each query, print numbers $ k,p_{1},p_{2},...,p_{k} $ separated by spaces in one line.

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