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
import io, os
input = sys.stdin.buffer.readline
#input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline

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

from collections import deque
INF = 10**18
temp= INF
for a, b in edge:
    q = deque([])
    q.append(b)
    visit = [INF]*n
    visit[b] = 0
    par = [-1]*n
    while q:
        v = q.popleft()
        for u in g[v]:
            if visit[u] == INF:
                visit[u] = visit[v]+1
                par[u] = v
                q.append(u)
    if visit[a]+1 <= temp:
        ans = []
        v = a
        ans.append(v+1)
        while par[v] != -1:
            v = par[v]
            ans.append(v+1)
        temp =  visit[a]+1

if temp == INF:
    print(-1)
else:
    if ans:
        print(len(ans))
        print(*ans, sep='\n')
    else:
        print(-1)