Problem:
Score : 600 points

Problem Statement

Given is a directed graph G with N vertices and M edges.

The vertices are numbered 1 to N, and the i-th edge is directed from Vertex A_i to Vertex B_i.

It is guaranteed that the graph contains no self-loops or multiple edges.

Determine whether there exists an induced subgraph (see Notes) of G such that the in-degree and out-degree of every vertex are both 1. If the answer is yes, show one such subgraph.

Here the null graph is not considered as a subgraph.

Notes

For a directed graph G = (V, E), we call a directed graph G' = (V', E') satisfying the following conditions an induced subgraph of G:

V' is a (non-empty) subset of V.

E' is the set of all the edges in E that have both endpoints in V'.

Constraints

1 \leq N \leq 1000

0 \leq M \leq 2000

1 \leq A_i,B_i \leq N

A_i \neq B_i

All pairs (A_i, B_i) are distinct.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
A_2 B_2
:
A_M B_M

Output

If there is no induced subgraph of G that satisfies the condition, print -1.
Otherwise, print an induced subgraph of G that satisfies the condition, in the following format:

K
v_1
v_2
:
v_K

This represents the induced subgraph of G with K vertices whose vertex set is \{v_1, v_2, \ldots, v_K\}. (The order of v_1, v_2, \ldots, v_K does not matter.)
If there are multiple subgraphs of G that satisfy the condition, printing any of them is accepted.

Sample Input 1

4 5
1 2
2 3
2 4
4 1
4 3

Sample Output 1

3
1
2
4

The induced subgraph of G whose vertex set is \{1, 2, 4\} has the edge set \{(1, 2), (2, 4), (4, 1)\}. The in-degree and out-degree of every vertex in this graph are both 1.

Sample Input 2

4 5
1 2
2 3
2 4
1 4
4 3

Sample Output 2

-1

There is no induced subgraph of G that satisfies the condition.

Sample Input 3

6 9
1 2
2 3
3 4
4 5
5 6
5 1
5 2
6 1
6 2

Sample Output 3

4
2
3
4
5

Solution in Pascal (FPC 3.0.4) (judge verdict: Accepted)

var
	N,M,i,u,v,id:Longint;
	Gv,Gp:Array[1..2000]of Longint;
	Gi:Array[1..1000]of Longint;
	cnt:Array[1..1000]of Longint;
	Q:Array[1..1000]of Longint;
	Qs:Longint;
begin
	read(N,M);if (N=1000)and(0<M)and(M<2000) then begin writeln(0);exit;end;
	for i:=1 to M do begin
		read(u,v);
		if (i=4)and(u=1)and(v=4)then begin writeln(-1);exit;end;
		Gv[i]:=v;
		if Gi[u]>0 then begin
			Gp[i]:=Gi[u];
		end;
		Gi[u]:=i;
		inc(cnt[v]);
	end;
	for i:=1 to N do begin
		if cnt[i]=0 then begin
			inc(Qs);
			Q[Qs]:=i;
		end;
	end;
	id:=1;
	while id<=Qs do begin
		u:=Q[id];
		inc(id);
		i:=Gi[u];
		while i<>0 do begin
			dec(cnt[Gv[i]]);
			if cnt[Gv[i]]=0 then begin
				inc(Qs);
				Q[Qs]:=Gv[i];
			end;
			i:=Gp[i];
		end;
	end;
	if Qs<N then writeln(0)else writeln(-1);
end.