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4 초 (추가 시간 없음) 1024 MB 115 41 32 31.068%

문제

In RUN-land, there are $n$ cities numbered $1$ to $n$. Some pairs of cities are connected by a bidirectional road. It happens that there are $n-1$ roads in total and that for any two cities, and there is a unique path from one to the other.

The city number $1$ is the capital. Initially all roads have no color. Alex, the king of RUN-land asks you to perform the following query $Q$ times.

  • $u\ c\ m$: Given a city $u$, a color $c$, and an integer $m$, color all the roads on the unique path from $u$ to the capital in the color $c$. Even if a road already has a color, change its color to $c$. After coloring, compute the number of colors in which exactly $m$ roads are colored.

Given $Q$ queries in total, compute the answer for the second part of each query.

입력

The first line of the input contains three integers $n,\ C,\ Q$ ($1\leq n,\ C,\ Q\leq 200,000$), separated by a single space, which are the number of cities in RUN-land, the number of possible colors, and the number of queries, respectively. Each of the next $n-1$ lines contains two integers $u,\ v$ ($1\leq u,\ v\leq n$) meaning that there is a bidirectional road directly connecting the cities numbered $u$ and $v$.

Each of the next $Q$ lines contains a query, which contains $3$ integers $u,\ c,\ m$ as described in the statement. ($1\leq u\leq n$, $1\leq c\leq C$, $0\leq m\leq n-1$)

출력

Print $Q$ lines, one for each query. Each line must contain one integer, the answer to the corresponding query.

예제 입력 1

6 5 5
1 3
2 3
1 4
6 3
5 2
5 1 3
6 2 2
2 3 1
4 4 1
1 5 0

예제 출력 1

1
2
2
3
1

The answer for the last query is $1$ since color $5$ is used in $0$ roads.