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())
graph = [[] for _ in range(n+1)]
indeg = [0] * (n+1)
outdeg = [0] * (n+1)
for _ in range(m):
    a, b = map(int, input().split())
    graph[a].append(b)
    indeg[b] += 1
    outdeg[a] += 1

is_valid = [indeg[i] * outdeg[i] for i in range(n+1)]
u = n+10
ans = []
from collections import deque
for start in range(1, n+1):
    if not is_valid[start]:
        continue

    # print("start: ", start, "---------")
    q = deque([start])
    visited = [False] * (n+1)
    prev = [-1] * (n+1)
    visited[start] = True

    has_ans = False
    while q:
        now = q.popleft()
        # print("now", now)
        for node in graph[now]:
            if node == start:
                # print("roop")
                prev[node] = now
                has_ans = True
                break
            if visited[node] or not is_valid[node]:
                continue
            # print("  to: ", node)
            prev[node] = now
            visited[node] = True
            q.append(node)
        if has_ans:
            break

    if not has_ans:
        continue
    cnt = 0
    tmp = []
    now = start
    for _ in range(n):
        tmp.append(now)
        cnt += 1
        now = prev[now]
        if now == start or now == -1:
            break
    if cnt < u:
        u = cnt
        ans = tmp

if ans:
    print(u)
    for t in ans:
        print(t)
else:
    print(-1)