BOTTOM - The Bottom of a Graph
题意翻译
## 题目描述：
V个点，E条单向边，定义link点：一个点u所能到达的点，反过来都能到达u，那么点u就是link点。升序输出所有的link点。
## 输入输出格式
### 输入格式：
多组数据直到V=0时结束
每组数据第一行是$V,E\: (1<=V<=5000)$
第二行是$v_1,w_1,v_2,w_2...v_E,w_E$
其中$v_i,w_i$表示从$v_i$到$w_i$的一条有向边
### 输出格式：
对于每组数据，一行内升序输出符合题面要求的点的序号（每个后面加个空格）。如果这样的点不存在，则输出一个空行。
## 输入输出样例
### 输入样例：
```
3 3
1 3 2 3 3 1
2 1
1 2
0
```
### 输出样例：
```
1 3
2
```
题目描述
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We will use the following (standard) definitions from graph theory. Let $V$ be a nonempty and finite set, its elements being called vertices (or nodes). Let $E$ be a subset of the Cartesian product $V \\times V$, its elements being called edges. Then $G = (V, E)$ is called a directed graph.
Let $n$ be a positive integer, and let $p = (e\_1, \\ldots, e\_n)$ be a sequence of length $n$ of edges $e\_i \\in E$ such that $e\_i = (v\_i, v\_{i+1})$ for a sequence of vertices ($v\_1, \\ldots, v\_{n+1}$). Then $p$ is called a path from vertex $v\_1$ to vertex $v\_{n+1}$ in $G$ and we say that $v\_{n+1}$ is reachable from $v\_1$, writing $(v\_1 \\to v\_{n+1})$.
Here are some new definitions. A node $v$ in a graph $G = (V, E)$ is called a sink, if for every node $w$ in $G$ that is reachable from $v$, $v$ is also reachable from $w$. The bottom of a graph is the subset of all nodes that are sinks, i.e., $\\mathrm{bottom}(G) = \\{v \\in V \\mid \\forall w \\in V : (v \\to w) \\Rightarrow (w \\to v) \\}$. You have to calculate the bottom of certain graphs.