Sinks of a Graph

You are given a directed graph $G = (V, E)$.

For any two nodes $u, v \in V$, if there is a path from $u$ to $v$ using only edges in $E$, we write $u \to v$.

A node $v \in V$ is called a sink if every node reachable from $v$ has a path back to $v$; that is, if it satisfies the following condition:

$\forall w \in V,\ (v \to w) \implies (w \to v)$

The set of all sinks of $G$ is denoted $\mathrm{bottom}(G)$.

$\mathrm{bottom}(G) = \{\, v \in V : \forall w \in V,\ (v \to w) \implies (w \to v) \,\}$

Given the graph $G = (V, E)$, compute $\mathrm{bottom}(G)$.

The input consists of several test cases.

The first line of each test case contains the number of nodes $n$ ($1 \le n \le 5\,000$) and a non-negative integer $m$ ($0 \le m \le 100\,000$). This means $V = \{1, 2, \dots, n\}$ and the number of edges is $|E| = m$.

Then follow $m$ integer pairs $v_1\ w_1\ v_2\ w_2\ \dots\ v_m\ w_m$ separated by whitespace, where each pair $(v_i, w_i)$ denotes an edge $(v_i, w_i) \in E$. These integers may span multiple lines.

The input ends with a value of $n$ equal to $0$; such a test case must not be processed, and the program should terminate.

For each test case, print all nodes in $\mathrm{bottom}(G)$ on one line, sorted in ascending order and separated by spaces. If $\mathrm{bottom}(G)$ is empty, print an empty line.