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

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

seen = [0] * n
checked = [0] * n
hist = deque()
ret = -1
def dfs(v):
    global ret
    seen[v] = 1
    hist.append(v)
    for nv in edge[v]:
        if checked[nv]: 
            continue
        if seen[nv] and not checked[nv]:
            ret = nv
            return
        dfs(nv)
        if ret != -1: 
            return
    hist.pop()
    checked[v] = 1

for i in range(n):
    dfs(i)
    if ret != -1:
        break

if ret == -1:
    print(-1)
    exit()

cycle = []
while hist:
    t = hist.pop()
    cycle.append(t)
    if t == ret:
        break
cycle.reverse()

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[:]