A11959 · Two-Paths · GESP考级

题目描述

You are given a weighted tree (undirected connected graph with no cycles, loops or multiple edges) with $n$ vertices. The edge $\{u_j, v_j\}$ has weight $w_j$ . Also each vertex $i$ has its own value $a_i$ assigned to it. Let's call a path starting in vertex $u$ and ending in vertex $v$ , where each edge can appear no more than twice (regardless of direction), a 2-path. Vertices can appear in the 2-path multiple times (even start and end vertices). For some 2-path $p$ profit $\text{Pr}(p) = \sum\limits_{v \in \text{distinct vertices in } p}{a_v} - \sum\limits_{e \in \text{distinct edges in } p}{k_e \cdot w_e}$ , where $k_e$ is the number of times edge $e$ appears in $p$ . That is, vertices are counted once, but edges are counted the number of times they appear in $p$ . You are about to answer $m$ queries. Each query is a pair of vertices $(qu, qv)$ . For each query find 2-path $p$ from $qu$ to $qv$ with maximal profit $\text{Pr}(p)$ .

The first line contains two integers $n$ and $q$ ( $2 \le n \le 3 \cdot 10^5$ , $1 \le q \le 4 \cdot 10^5$ ) — the number of vertices in the tree and the number of queries. The second line contains $n$ space-separated integers $a_1, a_2, \dots, a_n$ $(1 \le a_i \le 10^9)$ — the values of the vertices. Next $n - 1$ lines contain descriptions of edges: each line contains three space separated integers $u_i$ , $v_i$ and $w_i$ ( $1 \le u_i, v_i \le n$ , $u_i \neq v_i$ , $1 \le w_i \le 10^9$ ) — there is edge $\{u_i, v_i\}$ with weight $w_i$ in the tree. Next $q$ lines contain queries (one per line). Each query contains two integers $qu_i$ and $qv_i$ $(1 \le qu_i, qv_i \le n)$ — endpoints of the 2-path you need to find.

For each query print one integer per line — maximal profit $\text{Pr}(p)$ of the some 2-path $p$ with the corresponding endpoints.

输入 #1

7 6
6 5 5 3 2 1 2
1 2 2
2 3 2
2 4 1
4 5 1
6 4 2
7 3 25
1 1
4 4
5 6
6 4
3 4
3 7

输出 #1