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: Runtime Error)

import sys
input = sys.stdin.readline

N, M = map(int, input().split())
G = [[] for _ in range(N+1)]
for _ in range(M):
    A, B = map(int, input().split())
    G[A].append(B)

def dfs(v, o):
    ret = None
    for c in G[v]:
        if c == o:
            return [v]
    else:
        for c in G[v]:
            ret = dfs(c, o)
            if ret:
                return [v] + ret

for v in range(1, N+1):
    cur = dfs(v, v)
    if cur:
        break
else:
    print(-1)
    exit()

while True:
    cur_set = set(cur)
    unused = None
    for i in range(len(cur)):
        u, v = cur[i], cur[(i+1) % len(cur)]
        for c in G[u]:
            if c == v:
                continue
            elif c in cur_set:
                unused = (i, cur.index(c))
                break

    if not unused:
        break
    else:
        t, s = unused
        nxt = []
        i = s
        while i != t:
            nxt.append(cur[i])
            i = (i + 1) % len(cur)
        nxt.append(cur[t])
        cur = nxt
print(len(cur))
print(*cur, sep='\n')