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 = map(int, input().split())
ab = [list(map(int, input().split())) for _ in range(m)]
INF = 10 ** 5

adj = [[] for _ in range(n)]
for a, b in ab:
    a -= 1
    b -= 1
    adj[a].append(b)

mn = INF
for s in range(n):
    dq = deque([s])
    d = [-1] * n
    p = [-1] * n
    d[s] = 0
    last = []

    while dq:
        u = dq.popleft()
        for v in adj[u]:
            if d[v] == -1:
                d[v] = d[u] + 1
                p[v] = u
                dq.append(v)

            if v == s:
                last.append(u)

    for v in last:
        route = [v]
        while p[v] != s:
            v = p[v]
            route.append(v)

        route.append(s)
        size = len(route)
        if size < mn:
            mn = size
            ans = route[::-1]

if mn != INF:
    print(mn)
    for e in ans:
        print(e + 1)
else:
    print(-1)