102674: [AtCoder]ABC267 E - Erasing Vertices 2

Problem Statement

You are given a simple undirected graph with $N$ vertices and $M$ edges. The $i$-th edge connects Vertices $U_i$ and $V_i$. Vertex $i$ has a positive integer $A_i$ written on it.

You will repeat the following operation $N$ times.

• Choose a Vertex $x$ that is not removed yet, and remove Vertex $x$ and all edges incident to Vertex $x$. The cost of this operation is the sum of the integers written on the vertices directly connected by an edge with Vertex $x$ that are not removed yet.

We define the cost of the entire $N$ operations as the maximum of the costs of the individual operations. Find the minimum possible cost of the entire operations.

Constraints

• $1 \le N \le 2 \times 10^5$
• $0 \le M \le 2 \times 10^5$
• $1 \le A_i \le 10^9$
• $1 \le U_i,V_i \le N$
• The given graph is simple.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$
$A_1$ $A_2$ $\dots$ $A_N$
$U_1$ $V_1$
$U_2$ $V_2$
$\vdots$
$U_M$ $V_M$

Output

Print the answer.

Sample Input 1

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

Sample Output 1

3

By performing the operations as follows, the maximum of the costs of the $N$ operations can be $3$.

• Choose Vertex $3$. The cost is $A_1=3$.
• Choose Vertex $1$. The cost is $A_2+A_4=3$.
• Choose Vertex $2$. The cost is $0$.
• Choose Vertex $4$. The cost is $0$.

The maximum of the costs of the $N$ operations cannot be $2$ or less, so the solution is $3$.

Sample Input 2

7 13
464 661 847 514 74 200 188
5 1
7 1
5 7
4 1
4 5
2 4
5 2
1 3
1 6
3 5
1 2
4 6
2 7

Sample Output 2

1199

问题描述

给你一个有N个顶点和M条边的简单无向图。第i条边连接顶点U_i和V_i。顶点i上写有一个正整数A_i。

你将重复执行N次以下操作：

• 选择一个尚未被移除的顶点x，并移除顶点x和所有与顶点x相邻的边。该操作的费用是顶点x直接连接的顶点中尚未被移除的顶点上的整数之和。

我们定义N次操作的总费用为每次操作的费用的最大值。找出总操作的最低可能费用。

约束

• 1≤N≤2×10^5
• 0≤M≤2×10^5
• 1≤A_i≤10^9
• 1≤U_i,V_i≤N
• 给定的图是简单的。
• 输入中的所有值都是整数。

输入

输入格式如下：

N M
A_1 A_2 … A_N
U_1 V_1
U_2 V_2
⋮
U_M V_M

输出

打印答案。

样例输入1

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

样例输出1

3

按照以下方式执行操作，N次操作的最大费用可以为3。

• 选择顶点3。费用为A_1=3。
• 选择顶点1。费用为A_2+A_4=3。
• 选择顶点2。费用为0。
• 选择顶点4。费用为0。

N次操作的最大费用不能为2或更小，所以解决方案为3。

样例输入2

7 13
464 661 847 514 74 200 188
5 1
7 1
5 7
4 1
4 5
2 4
5 2
1 3
1 6
3 5
1 2
4 6
2 7

样例输出2

1199