题目描述

The $N$ cows ($2 \le N \le 1,000$) conveniently numbered $1$…$N$ are grazing among the $N$ pastures also conveniently numbered $1$…$N$. Most conveniently of all, cow $i$ is grazing in pasture $i$.

Some pairs of pastures are connected by one of $N-1$ bidirectional walkways that the cows can traverse. Walkway $i$ connects pastures $A_i$ and $B_i$ ($1 \le A_i \le N; 1 \le B_i \le N$) and has a length of $L_i$ ($1 \le L_i \le 10,000$).

The walkways are set up in such a way that between any two distinct pastures, there is exactly one path of walkways that travels between them. Thus, the walkways form a tree.

The cows are very social and wish to visit each other often. Ever in a hurry, they want you to help them schedule their visits by computing the lengths of the paths between $1 \le L_i \le 10,000$ pairs of pastures (each pair given as a query $p1$,$p2$ ($1 \le p1 \le N; 1 \le p2 \le N$).

POINTS: 200

有$N$（$2 \le N \le 1,000$）头奶牛，编号为 $1$ 到 $N$，它们正在同样编号为 $1$ 到 $N$ 的牧场上行走.为了方便，我们假设编号为 $i$ 的牛恰好在第 $i$ 号牧场上。

有一些牧场间每两个牧场用一条双向道路相连，道路总共有 $N - 1$ 条，奶牛可以在这些道路上行走。第i条道路把第 $A_i$ 个牧场和第 $B_i$ 个牧场连了起来（$1 \le A_i \le N; 1 \le B_i \le N$），而它的长度是 $1 \le L_i \le 10,000$ 在任意两个牧场间，有且仅有一条由若干道路组成的路径相连。也就是说，所有的道路构成了一棵树。

奶牛们十分希望经常互相见面。它们十分着急，所以希望你帮助它们计划它们的行程，你只 需要计算出 $Q$（$1 < Q < 1000$）对点之间的路径长度。每对点以一个询问 $p1$，$p2$ ($1 \le p1 \le N; 1 \le p2 \le N$) 的形式给出。

输入格式

* Line 1: Two space-separated integers: $N$ and $Q$

* Lines $2$…$N$: Line $i+1$ contains three space-separated integers: $A_i$, $B_i$, and $L_i$

* Lines $N+1$…$N+Q$: Each line contains two space-separated integers representing two distinct pastures between which the cows wish to travel: $p1$ and $p2$

输出格式

* Lines $1$…$Q$: Line $i$ contains the length of the path between the two pastures in query $i$.

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

2 
7 

提示

Query 1: The walkway between pastures $1$ and $2$ has length $2$.

Query 2: Travel through the walkway between pastures $3$ and $4$, then the one between $4$ and $1$, and finally the one between $1$ and $2$, for a total length of $7$.