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
input = sys.stdin.readline
sys.setrecursionlimit(10**7)
n, m = map(int, input().split())
G = [[] for _ in range(n)]
for i in range(m):
  a, b = map(int, input().split())
  a -= 1
  b -= 1
  G[a].append(b)
seen = [False]*n
def dfs(v):
  seen[v] = True
  for nv in G[v]:
    nxt[v] = nv
    if seen[nv]:
      return nv
    s = dfs(nv)
    if s != -1:
      return s
  seen[v] = False
  return -1
for i in range(n):
  nxt = [-1]*n
  s = dfs(i)
  if s != -1:
    break
else:
  print(-1)
  exit()
while True:
  used = set()
  L = []
  while s not in used:
    used.add(s)
    L.append(s)
    s = nxt[s]
  L.append(s)
  for i in range(len(L)-1):
    a, b = L[i], L[i+1]
    for nv in G[a]:
      if nv != b and nv in used:
        nxt[a] = nv
        s = a
        break
    else:
      continue
    break
  else:
    print(len(used))
    for v in used:
      print(v+1)
    break