16181번 - Coloring Roads 다국어

문제

In RUN-land, there are $n$ cities numbered 1ドル$ 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ドル$ 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,ドル a color $c,ドル and an integer $m,ドル 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ドル\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ドル\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ドル$ integers $u,\ c,\ m$ as described in the statement. (1ドル\leq u\leq n,ドル 1ドル\leq c\leq C,ドル 0ドル\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.

제한

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