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:
N,M=map(int,input().split())
data=[[] for i in range(N+1)]
for i in range(M):
    A,B=map(int,input().split())
    data[A].append(B)
lst=[]
for i in range(1,N+1):
    flag=[0]*(N+1)
    parent=[0]*(N+1)
    que=[i]
    while que:
        h=[]
        for u in que:
            for v in data[u]:
                if flag[v]==0:
                    flag[v]=1
                    parent[v]=u
                    h.append(v)
        que=h
    if parent[i]==0:
        continue
    lsls=[i]
    zzz=i
    while True:
        zzz=parent[zzz]
        if zzz==i:
            break
        lsls.append(zzz)
    lst.append(lsls)
inf=float("inf")
k=inf
ans=None
for u in lst:
    if k>len(u):
        ans=u
        k=len(u)
if k==inf:
    print(-1)
else:
    print(k)
    for v in ans:
        print(v)