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())
AB = [tuple(map(int,input().split())) for i in range(M)]
es = [[] for i in range(N)]
for a,b in AB:
    a,b = a-1,b-1
    es[a].append(b)

from collections import deque
tmpdist = N
ans = None
for to in range(N):
    for fr in es[to]:
        dist = [N] * N
        dist[fr] = 0
        prev = [-1] * N
        q = deque([fr])
        while q:
            v = q.popleft()
            if v==to: break
            for w in es[v]:
                if dist[w] < N: continue
                if v==to and w==fr: continue
                dist[w] = dist[v] + 1
                prev[w] = v
                q.append(w)
        else:
            continue
        if dist[to] < tmpdist:
            tmpdist = dist[to]
            ans = set()
            v = to
            while 1:
                ans.add(v+1)
                if prev[v] < 0: break
                v = prev[v]
if ans is None:
    print(-1)
else:
    print(len(ans))
    print(*ans, sep='\n')