The Bottom of a Graph
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 V×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, ..., e_n) be a sequence of length n of edges e_i E such that e_i = (v_i, v_{i+1}) for a sequence of vertices (v_1, ..., 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 → 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.,
bottom(G) = {v V | (w V )v → w w → v}.
Your task is to calculate the bottom of certain graphs.
Input
The input contains several test cases, each of which corresponds to a directed graph G. Each test case starts with an integer number v, denoting the number of vertices of G = (V, E), where the vertices will be identified by the integer numbers in the set V = {1, ..., v}. You may assume that 1 ≤ v ≤ 5000. That is followed by a non-negative integer eand then e pairs of vertex identifiers v_1, w_1, ..., v_e, w_e with the meaning that (v_i, w_i) E. There are no edges other than specified by these pairs. The last test case is followed by a zero.
Output
For each test case output the bottom of the specified graph on a single line. To this end, print the numbers of all nodes that are sinks in sorted order separated by a single space character. If the bottom is empty, print an empty line.