CF553D.Nudist Beach

Nudist Beach is planning a military operation to attack the Life Fibers. In this operation, they will attack and capture several cities which are currently under the control of the Life Fibers.

There are n cities, labeled from 1 to n, and m bidirectional roads between them. Currently, there are Life Fibers in every city. In addition, there are k cities that are fortresses of the Life Fibers that cannot be captured under any circumstances. So, the Nudist Beach can capture an arbitrary non-empty subset of cities with no fortresses.

After the operation, Nudist Beach will have to defend the captured cities from counterattack. If they capture a city and it is connected to many Life Fiber controlled cities, it will be easily defeated. So, Nudist Beach would like to capture a set of cities such that for each captured city the ratio of Nudist Beach controlled neighbors among all neighbors of that city is as high as possible.

More formally, they would like to capture a non-empty set of cities S with no fortresses of Life Fibers. The strength of a city is defined as (number of neighbors of x in S) / (total number of neighbors of x). Here, two cities are called neighbors if they are connnected with a road. The goal is to maximize the strength of the weakest city in S.

Given a description of the graph, and the cities with fortresses, find a non-empty subset that maximizes the strength of the weakest city.

“裸体海滩”正计划开展一次军事行动，以进攻并占领“生命纤维”当前控制的若干城市。

共有 $n$ 座城市，编号从 $1$ 到 $n$，以及它们之间连接的 $m$ 条双向道路。目前，每座城市中都存在“生命纤维”。此外，还有 $k$ 座城市是“生命纤维”的堡垒，无论如何都无法被攻占。因此，“裸体海滩”可任意选择一个非空的城市子集进行占领，但该子集中不能包含任何堡垒城市。

行动结束后，“裸体海滩”需防御所占领的城市，抵御敌方反扑。若某座被占领的城市与大量仍由“生命纤维”控制的城市相邻，则该城极易被击溃。因此，“裸体海滩”希望选择一组城市，使得对其中每一座被占领的城市而言，其所有邻居中由“裸体海滩”控制的邻居所占比例尽可能高。

更形式化地：他们希望选出一个非空的城市集合 $S$，且 $S$ 中不包含任何“生命纤维”的堡垒城市。对于任意城市 $x \in S$，其强度（strength） 定义为

$$\frac{\text{城市 } x \text{ 在 } S \text{ 中的邻居数量}}{\text{城市 } x \text{ 的邻居总数}}.$$

这里，若两座城市之间有道路直接相连，则称它们互为邻居。目标是最大化集合 $S$ 中最弱城市（即强度最小的城市）的强度。

给定图的结构描述以及所有堡垒城市，请找出一个满足条件的非空子集，使得其中最弱城市的强度达到最大。

The first line of input contains three integers n, m, k (2  ≤  n  ≤ 100 000, 1 ≤ m ≤ 100 000, 1 ≤ k ≤ n - 1).

The second line of input contains k integers, representing the cities with fortresses. These cities will all be distinct.

The next m lines contain the roads. The i-th of these lines will have 2 integers a__i, b__i (1 ≤ a__i, b__i ≤ n, a__i ≠ b__i). Every city will have at least one road adjacent to it.

There is no more than one road between each pair of the cities.

输入的第一行包含三个整数 $n$、$m$、$k$（$2 \leq n \leq 100\,000$，$1 \leq m \leq 100\,000$，$1 \leq k \leq n-1$）。

输入的第二行包含 $k$ 个整数，表示建有堡垒的城市。这些城市互不相同。

接下来的 $m$ 行描述道路。其中第 $i$ 行包含两个整数 $a_i$、$b_i$（$1 \leq a_i, b_i \leq n$，$a_i \neq b_i$）。每个城市至少与一条道路相连。

任意两个城市之间至多只有一条道路。

The first line should contain an integer r, denoting the size of an optimum set (1 ≤ r ≤ n - k).

The second line should contain r integers, denoting the cities in the set. Cities may follow in an arbitrary order. This line should not contain any of the cities with fortresses.

If there are multiple possible answers, print any of them.

第一行应包含一个整数 $r$，表示最优集合的大小（$1 \le r \le n - k$）。

第二行应包含 $r$ 个整数，表示该集合中的城市。城市的顺序可以任意。该行中不应包含任何建有堡垒的城市。

若存在多个可能的答案，输出其中任意一个即可。

The first example case achieves a strength of 1/2. No other subset is strictly better.

The second example case achieves a strength of 1. Note that the subset doesn't necessarily have to be connected.

第一个样例达到的强度为 $1/2$。不存在其他严格更优的子集。

第二个样例达到的强度为 $1$。注意，该子集不一定需要是连通的。