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 heapq


def dijkstra(adj, start):
    # adj: [[to, cost] * vertices], 0th index must be empty
    prev = [0] * len(adj)
    dist = [float('inf')] * len(adj)
    dist[start] = 0
    q = []
    heapq.heappush(q, [0, start])
    while q:
        min_dist, v_from = heapq.heappop(q)
        if min_dist > dist[v_from]:
            continue
        v_tos = adj[v_from]
        for v_to in v_tos:
            if min_dist + v_to[1] < dist[v_to[0]]:
                dist[v_to[0]] = min_dist + v_to[1]
                prev[v_to[0]] = v_from
                heapq.heappush(q, [dist[v_to[0]], v_to[0]])
    return dist, prev


N, M = map(int, input().split())
adj = [[] for _ in range(2 * N + 1)]
flg = 1
see = [0] * (N + 1)
for _ in range(M):
    A, B = map(int, input().split())
    adj[A].append([B, 1])
    adj[A].append([B + N, 1])

ans_best = []
len_ans = N+1
for start in range(1, N+1):
    if flg == 0:
        if see[start] == 0:
            continue
    ans = []
    dist, prev = dijkstra(adj, start)
    if dist[start + N] < 10 ** 10:
        k = start + N
        while k != start:
            k = prev[k]
            ans.append(k)
        if len(ans) < len_ans:
            ans_best = ans
            len_ans = len(ans)
            if flg:
                for a in ans:
                    see[a] = 1
                flg = 0

if len_ans == N+1:
    print(-1)
else:
    print(len_ans)
    for a in ans_best:
        print(a)