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

from collections import deque

d = N+1
flag = False
for i in range(N):
    for v in E[i]:
        q = deque()
        q.append(v)
        used = [N+1]*N
        used[v] = 1
        while q:
            temp = q.popleft()
            if used[temp] > d:
                break
            for u in E[temp]:
                if u == i and d > used[temp]+1:
                    d = used[temp]+1
                    memo = [temp, u]
                    q = deque()
                    flag = True
                    break
                elif u == i:
                    q = deque()
                    break
                if used[u] < N+1:
                    continue
                used[u] = used[temp]+1
                q.append(u)

import heapq
if flag:
    h = []
    dist = [N+1]*N
    dist[memo[1]] = 0
    for v in E[memo[1]]:
        heapq.heappush(h, (1, v))
    while True:
        temp = heapq.heappop(h)
        if dist[temp[1]] < N+1:
            continue
        dist[temp[1]] = temp[0]
        if temp[1] == memo[0]:
            break
        for v in E[temp[1]]:
            if dist[v] < N+1:
                continue
            heapq.heappush(h, (temp[0]+1, v))
    ans = [memo[0]]
    d = dist[memo[0]]-1
    prev = memo[0]
    while d >= 0:
        for i in range(N):
            if dist[i] == d and prev in E[i]:
                prev = i
                ans.append(i)
                d -= 1
                break
    print(len(ans))
    for i in ans:
        print(i+1)
else:
    print(-1)