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 EV×V , its elements being called edges. Then G = (V,E) is called a directed graph.

Let n be a positive integer, and let p = (e1, ..., en) be a sequence of length n of edges eiE such that ei = (vi, vi+1) for a sequence of vertices (v1, ..., vn+1). Then p is called a path from vertex v1 to vertex vn+1 in G and we say that vn+1 is reachable from v1, writing (v1 → vn+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 data

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 v1, w1, ..., ve, we with the meaning that (vi, wi)E. There are no edges other than specified by these pairs. The last test case is followed by a zero.

3 3
1 3 2 3 3 1
2 1
1 2
0

1 3
2