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:
import sys
from collections import deque
N, M = map(int, input().split())
edges = [[] for i in range(N)]
AB = []
for _ in range(M):
    a, b = map(int, input().split())
    edges[a-1].append(b-1)
    AB.append((a-1, b-1))
def BFS(s):
    prev = [-1]*N
    que = deque([s])
    while que:
        v = que.pop()
        for nv in edges[v]:
            if nv == s:
                prev[nv] = v
                return (s, prev)
            if prev[nv]<0:
                que.append(nv)
                prev[nv] = v
    return (-1, prev)
for v in range(N):
    v0, prev = BFS(v)
    if v0>=0:
        break
if v0<0:
    print(-1)
    sys.exit()
circle = set()
circle.add(v0)
pv = prev[v0]
while pv != v0:
    circle.add(pv)
    pv = prev[pv]
for a, b in AB:
    if a in circle and b in circle and prev[b] != a:
        pv = prev[b]
        while pv != a:
            circle.remove(pv)
            pv = prev[pv]
        prev[b] = a
print(len(circle))
for i in circle:
    print(i+1)