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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

n, m = map(int, input().split())
edges = [[] for _ in range(n)]
for _ in range(m):
    a, b = map(int, input().split())
    edges[a - 1].append(b - 1)

def find_loop(index, visited, cycle):
    visited[index] = True
    cycle.append(index)
    for i in edges[index]:
        if visited.get(i):
            return cycle[cycle.index(i):]
        ret = find_loop(i, visited, cycle)
        if ret:
            return ret
    visited[index] = False
    cycle.pop(-1)
    return None

def find_local_minimum(cycle):
    nxt = {i: j for (i, j) in zip(cycle, cycle[1:] + cycle[:1])}
    processed = set()
    i = cycle[0]
    while i not in processed:
        processed.add(i)
        for j in edges[i]:
            if j in nxt:
                k = nxt[i]
                while k != j:
                    l = nxt[k]
                    del nxt[k]
                    k = l
                nxt[i] = j
        i = nxt[i]
    start = next(iter(nxt))
    ret = [i]
    i = nxt[i]
    while i != start:
        ret.append(i)
        i = nxt[i]
    return ret

cycle = None
visited = {}
for start in range(n):
    if start not in visited:
        cycle = find_loop(start, visited, [])
        if cycle:
            break

if cycle:
    ret = find_local_minimum(cycle)
    print(len(ret))
    for i in ret:
        print(i + 1)
else:
    print(-1)