Problem: 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.

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.

Examples

Input

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


Output

3
1
2
4


Input

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


Output

-1


Input

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


Output

4
2
3
4
5

Solution (in PYTHON3):

Solution:
# -*- coding: utf-8 -*-
from collections import defaultdict
from collections import deque
import sys
# sys.setrecursionlimit(10**6)
buff_readline = sys.stdin.buffer.readline
readline = sys.stdin.readline

INF = 2**62-1


def read_int():
    return int(buff_readline())


def read_int_n():
    return list(map(int, buff_readline().split()))


def read_float():
    return float(buff_readline())


def read_float_n():
    return list(map(float, buff_readline().split()))


def read_str():
    return readline().strip()


def read_str_n():
    return readline().strip().split()


def error_print(*args):
    print(*args, file=sys.stderr)


def mt(f):
    import time

    def wrap(*args, **kwargs):
        s = time.time()
        ret = f(*args, **kwargs)
        e = time.time()

        error_print(e - s, 'sec')
        return ret

    return wrap


def slv(N, M, AB):

    g = defaultdict(list)
    for a, b in AB:
        g[a].append(b)

    def bfs(s):
        q = deque([s])
        done = {}
        done[s] = 0
        prev = {}
        goal = None
        while q:
            u = q.popleft()
            for v in g[u]:
                if v not in done:
                    done[v] = done[u] + 1
                    prev[v] = u
                    q.append(v)
                if v == s:
                    goal = u
                    break
        if goal is None:
            return None
        v = goal
        ans = [s]
        while v in prev:
            ans.append(v)
            v = prev[v]
        return ans

    ans = [0] * (2*N)
    for i in range(1, N+1):
        a = bfs(i)
        if a and len(ans) > len(a):
            ans = a
    if len(ans) == (2*N):
        print(-1)
        return
    print(len(ans))
    print(*ans, sep='\n')


def main():
    N, M = read_int_n()
    AB = [read_int_n() for _ in range(M)]
    slv(N, M, AB)


if __name__ == '__main__':
    main()