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: Time Limit Exceeded)

import sys
from collections import deque
from collections import defaultdict
import copy

n, m = map(int, sys.stdin.readline().split())
adj = [[] for _ in range(n+1)]
for _ in range(m):
    a, b = map(int, sys.stdin.readline().split())
    adj[a].append(b)


def searchRoute(i):
    global adj
    nexts = deque()
    route = [i]
    visited = set()
    result = []
    for x in adj[i]:
        if x < i:
            continue
        nroute = copy.copy(route)
        nvisited = copy.copy(visited)
        nexts.append((x, nroute, nvisited))
    while len(nexts) > 0:
        error = False
        found = False
        x, xroute, xvisited = nexts.popleft()
        xroute.append(x)
        xvisited.add(x)
        for y in adj[x]:
            if y < i:
                continue
            if y == i:
                found = True
                break
            if y in xvisited:
                break
            yroute = copy.copy(xroute)
            yvisited = copy.copy(xvisited)
            nexts.append((y, yroute, yvisited))
        if found:
            result = xroute
            break
    return result

heiro = []
for i in range(1, n+1):
    res = searchRoute(i)
    if len(res) > 0:
        heiro = res
        break

if len(heiro) == 0:
    print(-1)
    exit()
while True:
    visited = set()
    bp = [-1, -1]
    rt = defaultdict(int)
    for i in range(len(heiro)):
        visited.add(heiro[i])
        rt[heiro[i]] = i
        for j in adj[heiro[i]]:
            if j in visited and not (i == len(heiro) - 1 and j == heiro[0]):
                bp = [i, rt[j]]
                break
        if bp[0] != -1:
            break
    if bp[0] == -1:
        print(len(heiro))
        for i in heiro:
            print(i)
        exit()
    heiro = heiro[bp[1]:bp[0]+1]