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

read = sys.stdin.read

N, M = map(int, input().split())
if M != 0:
    AB = list(map(int, read().split()))
else:
    print(-1)
    exit()

graph = [[] for _ in range(N + 1)]
A = AB[::2]
B = AB[1::2]
A_s = set(A)
# 出次数が0の頂点はいらない。
needless = set(range(1, N + 1)) - A_s

for i, j in zip(A, B):
    if j not in needless:
        graph[i].append(j)


# cycleを少なくとも一つ検出する
def dfs(original_stack):
    checked = [False] * (N + 1)
    while original_stack:
        start = original_stack.pop()
        if checked[start]:
            continue
        checked[start] = True
        stack = [(start, [start])]
        while stack:
            v, route = stack.pop()
            for i in graph[v]:
                if i in route:
                    return route[route.index(i):]
                else:
                    stack.append((i, route + [i]))
                    checked[i] = True


v = dfs([i for i in range(1, N + 1) if graph[i]])
if not v:
    print(-1)
    exit()

while True:
    v_s = set(v)
    length = len(v)
    for i, (v_i, v_j) in enumerate(zip(v, v[1:] + [v[0]])):
        for j in graph[v_i]:
            if j != v_j and j in v_s:
                idx = v.index(j)
                if i < idx:
                    v = v[:i + 1] + v[idx:]
                else:
                    v = v[idx:i + 1]
                break
        else:
            continue
        break
    else:
        print(len(v))
        print('\n'.join(map(str, v)))
        exit()