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 sys import setrecursionlimit
setrecursionlimit(10000)
N, M = map(int, input().split())
table = [[] for _ in range(N)]
for _ in range(M):
    a, b = map(int, input().split())
    table[a-1].append(b-1)

visit = [False] * N
visit2 = [False] * N
g = []


def dfs(v):
    g.append(v)
    if visit[v]:
        return True
    visit[v] = True
    visit2[v] = True
    for u in table[v]:
        if dfs(u):
            return True
    g.pop()
    visit[v] = False
    return False


for i in range(N):
    g = []
    if not visit2[i]:
        if dfs(i):
            break
else:
    print(-1)
    exit()
print(0)
# ans = [v+1 for v in g[g.index(g[-1]):-1]]
# print(len(ans))
# print(*ans, sep="\n")