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

N, M, *AB = map(int, open(0).read().split())

E = [[] for _ in range(N + 1)]
for a, b in zip(*[iter(AB)] * 2):
    E[a].append(b)

shortest = N + 1
ans = []
for s in range(1, N + 1):
    D = [-1] * (N + 1)
    P = [-1] * (N + 1)

    D[s] = 0
    Q = deque([s])
    while Q:
        p = Q.popleft()
        for c in E[p]:
            if D[c] < 0:
                D[c] = D[p] + 1
                P[c] = p
                Q.append(c)

    for t in range(1, N + 1):
        if t == s or D[t] < 0:
            continue

        for v in E[t]:
            if v != s:
                continue

            T = [s]
            cur = t
            while cur != s:
                T.append(cur)
                cur = P[cur]

            if shortest > len(T):
                shortest = len(T)
                ans = T

if shortest == N + 1:
    print(-1)
else:
    print(len(ans))
    print("\n".join(map(str, ans)))