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:
from collections import deque
from copy import deepcopy


# detection of a cycle
def detect_cycle(N, repn):
    color = ['WHITE'] * (N + 1)
    unfinished_vertex = set([i for i in range(1, N + 1)])
    cycle = []
    Repn = deepcopy(repn)

    def dfs(u0):
        deq = deque([u0])
        color[u0] = 'GRAY'

        while deq != deque([]) and cycle == []:
            u = deq[-1]
            if len(Repn[u]) != 0:
                v = Repn[u].popleft()
                if color[v] == 'WHITE':
                    color[v] = 'GRAY'
                    deq.append(v)
                elif color[v] == 'GRAY':
                    cycle.append(v)
            else:
                deq.pop()
                color[u] = 'BLACK'
                unfinished_vertex.remove(u)

        return deq

    while cycle == [] and unfinished_vertex != set([]):
        u = unfinished_vertex.pop()
        unfinished_vertex.add(u)
        deq = dfs(u)
        #print('deq = {}, cycle = {}'.format(deq, cycle))
    #print('deq = {}'.format(deq))
    if cycle != []:
        v = cycle.pop()
        while True:
            u = deq.pop()
            cycle.append(u)
            if u == v:
                break
        cycle.reverse()
        return cycle # cycle = [v -> ... -> u (-> v)]
    else:
        return []

# one-step minimization of a cycle
def minimize_cycle(cycle, repn):
    length = len(cycle)
    cycle_idx = {u : i for i, u in enumerate(cycle)}
    minimized = False

    for i, u in enumerate(cycle):
        if minimized == True:
            break
        else:
            for v in repn[u]:
                if v in cycle_idx.keys():
                    j = cycle_idx[v]
                    if i + 1 == j:
                        continue
                    elif i == length - 1 and j == 0:
                        continue
                    elif i < j:
                        reduced_cycle = cycle[:(i + 1)] + cycle[j:]
                        minimized = True
                        break
                    else:
                        reduced_cycle = cycle[j:(i + 1)]
                        minimized = True
                        break

    if minimized == True:
        return reduced_cycle, minimized
    else:
        return cycle, minimized


def main():
    N, M = map(int, input().split())
    repn = [deque([]) for i in range(N + 1)]
    for _ in range(M):
        a, b = map(int, input().split())
        repn[a].append(b)

    cycle = detect_cycle(N, repn)
    #print('cycle detected: {}'.format(cycle))
    if cycle == []:
        print(-1)
        exit()

    minimized = True
    while minimized == True:
        cycle, minimized = minimize_cycle(cycle, repn)
        #print('cycle minimized: {}, {}'.format(minimized, cycle))

    print(len(cycle))
    for u in cycle:
        print(u)


if __name__ == '__main__':
    main()