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:
import sys
from collections import deque

read = sys.stdin.read
readline = sys.stdin.readline
readlines = sys.stdin.readlines
sys.setrecursionlimit(10 ** 9)
INF = 1 << 60
MOD = 1000000007


def main():
    N, M, *AB = map(int, read().split())
    G = [[] for _ in range(N)]
    for a, b in zip(*[iter(AB)] * 2):
        G[a - 1].append(b - 1)

    ans = []
    for i in range(N):
        queue = deque([i])
        dist = [-1] * N
        dist[i] = 0
        prev = [-1] * N
        while queue:
            v = queue.popleft()
            for nv in G[v]:
                if dist[nv] == -1:
                    dist[nv] = dist[v] + 1
                    prev[nv] = v
                    queue.append(nv)
        for j in range(N):
            if i == j or dist[j] == -1 or i not in G[j]:
                continue
            tmp = []
            k = j
            while k != -1:
                tmp.append(k)
                k = prev[k]

            if not ans or len(ans) > len(tmp):
                ans = tmp

    if ans:
        print(len(ans))
        for v in ans:
            print(v + 1)
    else:
        print(-1)

    return


if __name__ == '__main__':
    main()