题目描述

Alice and Bob are in charge of testing a new escape room! In this escape room, customers are trapped in a dungeon and have to explore the entire area. The dungeon consists of $n$ rooms connected by exactly $n-1$ corridors. It is possible to travel between any pair of rooms using these corridors.

Two of the dungeon rooms are special. One of these rooms contains a protective idol known as the "helix key´´. A different room contains a nasty "dome trap´´, which prevents the player from moving once activated. Entering the room with the trap before acquiring the key will result in the player being trapped in the dungeon forever. The player cannot start in the same room as the key or the trap.

There are $q$ different scenarios that Alice and Bob wish to examine. In the $i^{th}$ scenario, the player starts in room $s_i$, the key is in room $k_i$, and the trap is in room $t_i$. For each scenario, compute the minimum amount of time needed to explore the entire dungeon without getting trapped.

输入格式

The first line of input contains two integers $n$ and $q$, where $n$ ($3 \leq n \leq 2000$) is the number of rooms and $q$ ($1 \leq q \leq 200000$) is the number of scenarios to consider. Rooms are numbered from $1$ to $n$. The next $n-1$ lines each contain three integers $u$, $v$, and $w$ indicating that there is a corridor between rooms $u$ and $v$ ($1 \leq u, v \leq n, u \neq v$) that takes time $w$ ($1 \leq w \leq 10^9$) to traverse.

Then follow $q$ lines: the $i^{th}$ of these lines contains three distinct integers $s_i$, $k_i$, and $t_i$ ($1 \leq s_i, k_i, t_i \leq n$) indicating the room where the player starts, the room with the key, and the room with the trap, respectively.

输出格式

For each scenario, output the minimum amount of time needed to visit every room at least once. If it is impossible to visit every room at least once, output $\texttt{impossible}$.

题目大意

题目描述

有一棵 $n$ 个结点的树，边带权。你可以从一个结点通过边移动到一个相邻的结点，花费等同于边权的时间。

其中，有两个特殊结点，一个结点里有钥匙，一个结点里有陷阱。你只有先获得钥匙，才能进入陷阱所在的结点。

现有 $q$ 组询问，在第 $i$ 组询问中，你要从第 $s_i$ 号结点出发，钥匙在第 $k_i$ 号结点，陷阱在第 $t_i$ 号结点。你需要对于每组询问回答遍历整棵树所需的最短时间。题目保证你不会在钥匙所在的结点或者陷阱所在的结点出发。如果不可能遍历整棵树，输出 impossible。

输入格式

第一行两个整数 $n,q$，含义如题目所述。

接下来 $n-1$ 行，每行三个整数 $u,v,w$，表示有一条连接结点 $u,v$，权值为 $w$ 的边。

接下来 $q$ 行，每行三个整数 $s_i,k_i,t_i$，含义如题目所述。

$3\le n\le 2000$，$1\le q \le 2\times10^5$，$1\le u,v\le n,u\ne v$，$1\le w\le 10^9$，$1\le s_i,k_i,t_i\le n$。

输出格式

对于每组询问，输出一行，包含一个整数表示答案，或者输出 impossible 表示无解。

5 4
1 2 3
1 3 1
3 4 4
3 5 2
1 2 4
1 4 2
5 2 1
4 3 1

15
17
impossible
12

7 4
1 2 1
1 3 1
1 4 1
1 5 1
1 6 1
1 7 1
1 2 3
5 4 1
3 1 4
2 4 5

11
impossible
10
10