在做网络流之前，发生了一件非常有趣的事情。
我问蔡爷爷：“大佬，您做的网络流都好神，又神又劲$%%%$”

2561: 最小生成树

Description

　给定一个边带正权的连通无向图G=(V,E)，其中N=|V|，M=|E|，N个点从1到N依次编号，给定三个正整数u，v，和L (u≠v)，假设现在加入一条边权为L的边(u,v)，那么需要删掉最少多少条边，才能够使得这条边既可能出现在最小生成树上，也可能出现在最大生成树上？

Problem Description

There is a sequence a of length n. We use ai to denote the i-th element in this sequence. You should do the following three types of operations to this sequence.

0 x y t: For every x≤i≤y, we use min(ai,t) to replace the original ai’s value.
1 x y: Print the maximum value of ai that x≤i≤y.
2 x y: Print the sum of ai that x≤i≤y.

Query on a tree I

You are given a tree (an acyclic undirected connected graph) with N nodes, and edges numbered 1, 2, 3…N-1.
We will ask you to perfrom some instructions of the following form:
CHANGE i ti : change the cost of the i-th edge to ti
or
QUERY a b : ask for the maximum edge cost on the path from node a to node b

Query on a tree II

You are given a tree (an undirected acyclic connected graph) with N nodes, and edges numbered 1, 2, 3…N-1. Each edge has an integer value assigned to it, representing its length.
We will ask you to perfrom some instructions of the following form:
DIST a b : ask for the distance between node a and node b
KTH a b k : ask for the k-th node on the path from node a to node b

Query on a tree III

You are given a node-labeled rooted tree with n nodes.
Define the query (x, k): Find the node whose label is k-th largest in the subtree of the node x. Assume no two nodes have the same labels.
The first line contains one integer n (1 <= n <= 105). The next line contains n integers li (0 <= li <= 109) which denotes the label of the i-th node.
Each line of the following n - 1 lines contains two integers u, v. They denote there is an edge between node u and node v. Node 1 is the root of the tree.