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())
edges = [[] for _ in range(n)]

for _ in range(m):
    a, b = map(int, input().split())
    edges[a-1].append(b-1)


def get_first_cycle(n, edges):
    seen = [-1] * n  # seen: -1: 未確認, 0: 非cycleのnode, 1: cycle候補
    for start in range(n):
        if seen[start] == 0:
            continue
        seen[start] = 1
        path = [start]
        while path:
            now = path[-1]
            if not edges[now]:
                path.pop()
                seen[now] = 0
                continue

            next_node = edges[now].pop()
            if seen[next_node] == -1:
                path.append(next_node)
                seen[next_node] = 1

            elif seen[next_node] == 1:
                idx = path.index(next_node)
                cycle = path[idx:]
                return cycle
    return False


cycle = get_first_cycle(n, edges)
if not cycle:
    print(-1)
    exit()

nodes = set(cycle)
length = len(cycle)
i = 0
while i < length:
    now = cycle[i]
    routes = edges[now]
    while routes:
        to = routes.pop()
        if to in nodes:
            update = True
            idx = cycle.index(to)
            cycle = cycle[:i+1] + cycle[idx:]
            nodes = set(cycle)
            length = len(cycle)
            break
    i += 1

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