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 defaultdict as dd
input = sys.stdin.readline
N, M = map(int, input().split())
e = dd(list)
reve = dd(list)
for _ in range(M):
  u, v = map(int, input().split())
  e[u].append(v)
  reve[v].append(u)
vis = set()
inc = [0] * (N + 1)
def dfs(x, l):
  global vis
  global inc
  vis.add(x)
  ok = 0
  for y in reve[x]:
    if y in vis: inc[x] += 1
  if inc[x] > 1:
    inc[x] = 0
    vis.discard(x)
    return
  for y in e[x]:
    if y == l:
      ok = 1
      continue
    if y in vis:
      inc[x] = 0
      vis.discard(x)
      return
  if ok:
    print(len(vis))
    for v in vis: print(v)
    #print(vis, inc)
    exit(0)
  for y in e[x]:
    dfs(y, l)
  vis.discard(x)

for s in range(1, N + 1):
  dfs(s, s)
print(-1)