CF1787G.Colorful Tree Again

An edge-weighted tree of $n$ nodes is given with each edge colored in some color. Each node of this tree can be blocked or unblocked, all nodes are unblocked initially.

A simple path is a path in a graph that does not have repeating nodes. The length of a path is defined as the sum of weights of all edges on the path.

A path is good when it is a simple path consisting of edges of the same color $c$, all edges of color $c$ are on this path, and every node on the path is unblocked.

You need to operate $2$ kinds of queries:

1. block a node,
2. unblock a node.

After each query, print the maximum length among all good paths. If there are no good paths, print $0$.

给定一棵含 $n$ 个节点的边带权树，每条边被染成某种颜色。该树的每个节点可以处于“阻塞”或“未阻塞”状态，初始时所有节点均为未阻塞。

简单路径（simple path）指图中不包含重复节点的路径。路径的长度定义为该路径上所有边的权重之和。

当一条路径满足以下条件时，称为好路径（good path）：

• 它是一条简单路径；
• 它仅由同一种颜色 $c$ 的边构成；
• 该颜色 $c$ 的所有边都出现在此路径上；
• 路径上的每个节点均处于未阻塞状态。

你需要处理两类操作查询：

1. 阻塞一个节点；
2. 解除一个节点的阻塞状态。

每次查询后，请输出当前所有好路径中的最大长度；若不存在任何好路径，则输出 $0$。

The first line contains two integers $n$, $q$ ($1 \leq n,q \leq 2\cdot 10^5$) — the number of nodes and the number of queries.

Then $n-1$ lines follow, each containing four integers $u$, $v$, $w$ and $c$ ($1 \leq u,v,w,c \leq n$; $u \not = v$), denoting a weighted edge connecting node $u$ and node $v$ with weight $w$ and color $c$. It is guaranteed that these edges form a tree.

Then $q$ lines follow, each containing two integers $p$ and $x$ ($p = 0$ or $p = 1$, $1\leq x\leq n$), denoting a query:

1. if $p = 0$, block the node $x$. It's guaranteed that it's not blocked at this time;
2. if $p = 1$, unblock the node $x$. It's guaranteed that it's blocked at this time.

第一行包含两个整数 $n$、$q$（$1 \leq n,q \leq 2\cdot 10^5$），分别表示节点数和查询数。

接下来 $n-1$ 行，每行包含四个整数 $u$、$v$、$w$ 和 $c$（$1 \leq u,v,w,c \leq n$；$u \neq v$），表示一条连接节点 $u$ 和节点 $v$ 的带权边，其权重为 $w$，颜色为 $c$。保证这些边构成一棵树。

接下来 $q$ 行，每行包含两个整数 $p$ 和 $x$（$p = 0$ 或 $p = 1$，$1\leq x\leq n$），表示一个查询：

1. 若 $p = 0$，则封锁节点 $x$；保证此时该节点尚未被封锁；
2. 若 $p = 1$，则解除对节点 $x$ 的封锁；保证此时该节点已被封锁。

For each query, print the maximum length of a good path. If there are no good paths, print $0$.

对于每个查询，输出一条好路径的最大长度。如果没有好路径，则输出 $0$。