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:
from collections import deque

N, M = map(int, input().split())
v = [[] for _ in range(N)]
for _ in range(M) :
    A, B = map(int, input().split())
    v[A-1].append(B-1)

def bfs(i) :
    dist = [float('inf')] * N
    pre = [-1] * N
    
    queue = deque([(i, 0)])
    while queue :
        cur, cost = queue.popleft()
        if dist[cur] < cost :
            continue
        for nex in v[cur] :                
            if cost + 1 < dist[nex] :
                dist[nex] = cost + 1
                pre[nex] = cur
                queue.append((nex, cost + 1))
    
    return dist[i], pre

mi = -1
mv = float('inf')
mp = []
for i in range(N) :
    m, pre = bfs(i)
    if m < mv :
        mi, mv, mp = i, m, pre

if mi >= 0 :
    print(mv)
    cur = mi
    while mp[cur] != mi :
        print(cur + 1)
        cur = mp[cur]
    print(cur + 1)
else :
    print(-1)