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:
n, m = map(int, input().split())
ans = [0] * (n + 1)
import collections
g = collections.defaultdict(set)

for _ in range(m):
    a, b = map(int, input().split())
    g[a-1].add(b-1)

def minCircle(s):
    f = [None] * n
    visited = set()
    q = []
    q.append(s)
    while q:
        node = q.pop()
        for nei in g[node]:
            if nei not in visited:
                f[nei] = node
                visited.add(nei)
                q.append(nei)
        if s in visited:
            break
    p = f[s]
    ret = []
    ret.append(s)
    while p is not None and p!= s:
        ret.append(p)
        p = f[p]
    return ret

for i in range(n):
    t = minCircle(i)
    if len(t) > 1 and len(t) < len(ans):
        ans = t
if len(ans) == n + 1:
    print(-1)
else:
    print(len(ans))
    for i in ans:
        print(i+1)