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 math
import sys
from collections import deque, defaultdict

N, M = map(int, input().split())
AB = [tuple(map(int, input().split())) for _ in range(M)]
g = [set() for _ in range(N)]
for a, b in AB:
    g[a - 1].add(b - 1)


def find_loop(s, subnode):
    q = deque([(s, {s})])
    visited = defaultdict(lambda: math.inf)
    while len(q) > 0:
        node, p = q.popleft()
        for to_node in g[node] & subnode:
            if to_node == s:
                return p
            if visited[to_node] > len(p):
                visited[to_node] = len(p)
                q.append((to_node, p | {to_node}))
    return -1


V = set(range(N))
for i in range(N):
    subnode = find_loop(i, V)
    if subnode != -1:
        break
if subnode == -1:
    print(-1)
    sys.exit()


while True:
    # 条件判定
    flg = True
    for i in subnode:
        if len(g[i] & subnode) != 1:
            flg = False
            s = i
            break
    if flg:
        break
    subnode = find_loop(s, subnode)

print(len(subnode))
for node in subnode:
    print(node+1)