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


def main():
    # N = int(input())
    # N,= [int(a) for a in input().split()]
    # N, M = [int(a) for a in input().split()]

    # a = []
    # # b = []
    # c = []
    #
    # for _ in range(M):
    #     aa, bb = [int(a) for a in input().split()]
    #     cc = [int(a) for a in input().split()]
    #     a.append(aa)
    #     # b.append(bb)
    #     c.append(cc)
    N, M = [int(a) for a in input().split()]

    AB = [
        [int(a) for a in input().split()]
        for _ in range(M)
    ]

    pp = [[] for _ in range(N)]
    for a, b in AB:
        pp[a - 1].append(b - 1)

    startpool = set(range(N))

    result = None

    while len(startpool) != 0:
        start = min(startpool)

        q = deque([(start, [start])])
        renketu = {start}
        while len(q) != 0:
            p, history = q.popleft()
            target = pp[p]
            for t in target:
                if t in history:
                    if result is None:
                        result = history
                    elif len(result) > len(history) - history.index(t):
                        result = history[history.index(t):]
                if t not in renketu:
                    q.append([t, history + [t]])

                renketu.add(t)
        startpool -= renketu

    if result is not None:
        print(len(result))
        for a in result:
            print(a + 1)
        return
    else:
        print(-1)


if __name__ == "__main__":
    main()