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
sys.setrecursionlimit(10000000)
MOD = 10 ** 9 + 7
INF = 10 ** 15

from collections import deque,defaultdict,Counter
def main():
    N,M = map(int,input().split())
    G = [[] for _ in range(N)]
    G_rev = [[] for _ in range(N)]
    for _ in range(M):
        a,b = map(int,input().split())
        a -= 1
        b -= 1
        G[a].append(b)
        G_rev[b].append(a)
    
    s,g = None,None
    ans = INF
    q = deque([])
    for i in range(N):
        q.append(i)
        dist = [-1] * N
        dist[i] = 0
        while q:
            v = q.popleft()
            for e in G[v]:
                if i == e:
                    if ans > dist[v] + 1:
                        ans = dist[v] + 1
                        s,g = i,v
                elif dist[e] < 0:
                    dist[e] = dist[v] + 1
                    q.append(e)

    if ans == INF:
        print(-1)
    else:
        print(ans)
        q.append(s)
        dist = [-1] * N
        dist[s] = 0
        while q:
            v = q.popleft()
            for e in G[v]:
                if e == g:
                    dist[g] = dist[v] + 1
                    q.clear()
                    break
                elif dist[e] < 0:
                    dist[e] = dist[v] + 1
                    q.append(e)
        route = [g + 1]
        now = g
        while now != s:
            for e in G_rev[now]:
                if dist[e] == dist[now] - 1:
                    now = e
                    break
            route.append(now + 1)
        print('\n'.join(map(str,route)))
if __name__ == '__main__':
    main()