Colorful Tree Again

Description:

Input:

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.

Output:

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

Sample Input:

5 4
4 1 3 4
5 2 4 4
3 1 3 2
1 2 5 1
0 4
0 3
0 2
1 3

Sample Output:

5
5
0
3

Sample Input:

5 5
4 1 4 4
4 5 2 2
3 1 2 4
3 2 3 1
0 3
0 4
1 3
1 4
0 1

Sample Output:

2
0
3
6
3

Sample Input:

6 9
3 2 2 3
2 4 4 2
3 1 5 5
6 4 3 2
5 3 1 3
0 2
0 4
0 5
0 6
1 2
1 4
1 5
0 3
1 6

Sample Output:

5
5
5
5
5
5
5
0
7

Sample Input:

1 2
0 1
1 1

Sample Output:

0
0