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:
from collections import deque
import sys
sys.setrecursionlimit(10**6)

class DirectedGraph:
    def __init__(self, adj):
        self.n = len(adj)
        self.adj = adj
        self.is_asyclic = False
        self.max_path_len = None

    def topological_sort(self):
        indegree = [0] * self.n
        for vs in self.adj:
            for dest in vs:
                indegree[dest] += 1
        zero_v = []
        for v, indeg in enumerate(indegree):
            if indeg == 0:
                zero_v.append(v)
        max_path_len = 1
        tp_sorted = []
        to_be_added = []
        while True:
            while zero_v:
                v = zero_v.pop()
                tp_sorted.append(v)
                for dest in self.adj[v]:
                    indegree[dest] -= 1
                    if indegree[dest] == 0:
                        to_be_added.append(dest)
            if len(to_be_added) > 0:
                zero_v.extend(to_be_added)
                to_be_added = []
                max_path_len += 1
            else:
                break
        if len(tp_sorted) == self.n:
            self.is_asyclic = True
            self.max_path_len = max_path_len
            return tp_sorted
        else:
            self.is_asyclic = False
            return None

    def extract_cycle(self):
        self.seen = [0] * self.n
        self.checked = [0] * self.n
        self.hist = deque()
        self.node_in_cycle = -1

        def dfs(v):
            self.seen[v] = 1
            self.hist.append(v)
            for nv in self.adj[v]:
                if self.checked[nv]:
                    continue
                if self.seen[nv] and not self.checked[nv]:
                    self.node_in_cycle = nv
                    return
                dfs(nv)
                if self.node_in_cycle != -1:
                    return
            self.hist.pop()
            self.checked[v] = 1

        for i in range(self.n):
            if not self.checked[i]:
                dfs(i)
            if self.node_in_cycle != -1:
                break
        if self.node_in_cycle == -1:
            return []
        else:
            cycle = []
            while self.hist:
                t = self.hist.pop()
                cycle.append(t)
                if t == self.node_in_cycle:
                    break
            cycle.reverse()
            return cycle

n, m = [int(item) for item in input().split()]
edge = [[] for _ in range(n)]
for i in range(m):
    a, b = [int(item) - 1 for item in input().split()]
    edge[a].append(b)

DG = DirectedGraph(edge)
cycle = DG.extract_cycle()

if len(cycle) == 0:
    print(-1)
    exit()

while True:
    in_cycle = set(cycle)
    deg = [0] * n 
    for item in cycle:
        for v in edge[item]:
            if v in in_cycle:
                deg[v] += 1
    
    ok = True
    for i, item in enumerate(cycle):
        if deg[item] > 1:
            ok = False
            cur_id = start = i
    if ok:
        print(len(cycle))
        print("\n".join([str(item + 1) for item in cycle]))
        exit()

    ncycle = []
    cur = cycle[cur_id]
    while True:
        ncycle.append(cur)
        if cycle[start] in edge[cur]:
            break
        cur_id = (cur_id + 1) % len(cycle)
        cur = cycle[cur_id]
    cycle = ncycle[:]