Description

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×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,...,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

(v₁,...,v_n+1)

. Then

p

is called a path from vertex

v₁

to vertex

v_n+1

in

G

and we say that

v_n+1

is reachable from

v₁

, writing

(v₁→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)}

. You have 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

e

and, thereafter,

e

pairs of vertex identifiers

v₁,w₁,...,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.

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

1 3
2

Source

Ulm Local 2003