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
from collections import defaultdict

sys.setrecursionlimit(10 ** 6)
input = sys.stdin.readline

def main():
    def bfs(u):
        dist = [inf] * n
        cur = [u]
        pre = [-1] * n
        dist[u] = 0
        d = 0
        while cur:
            d += 1
            nxt = []
            for v in cur:
                for kv in to[v]:
                    if dist[kv] != inf: continue
                    dist[kv] = d
                    pre[kv] = v
                    nxt.append(kv)
            cur = nxt
        mn = [inf, -1]
        for v in range(n):
            if v == u: continue
            if u in to[v]:
                mn = min(mn, [dist[v], v])

        # print(dist)
        # print(mn)
        # print(pre)
        res = []
        v = mn[1]
        if mn[0] == inf:
            return [0] * (n + 1)
        for _ in range(mn[0] + 1):
            res.append(v)
            v = pre[v]
        return res

    inf = 10 ** 9
    n, m = map(int, input().split())
    to = defaultdict(set)
    for _ in range(m):
        u, v = map(int, input().split())
        to[u - 1].add(v - 1)
    ans = [0] * (n + 1)
    for u in range(n):
        res = bfs(u)
        if len(res) < len(ans):
            ans = res
    if len(ans) == n + 1:
        print(-1)
    else:
        print(len(ans))
        for u in ans:
            print(u + 1)

main()