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 = [int(x) for x in input().strip().split(" ")]

def dfs(v, l):
    for u in d[v]:
        if u in pvs:
            return l + [u]
        if u in vs:
            continue
        pvs.add(u)
        vs.add(u)
        ll = dfs(u, l + [u])
        pvs.remove(u)
        if ll:
            return ll
    return False

d = [set() for _ in range(N)]
for _ in range(M):
    a, b = [int(x) for x in input().strip().split(" ")]
    d[a-1].add(b-1)

vs = set()
for i in range(N):
    if i in vs:
        continue
    vs.add(i)
    pvs = set([i])
    loop = dfs(i, [i])
#    print(i, loop, vs)
    if loop:
        break

import sys
#print(loop)
if not loop:
    print("-1")
    sys.exit()
else:
    ll = []
    lx = loop[-1]
    f = False
    for x in loop:
        if lx == x and not f:
            f = True
            continue
        if not f:
            continue
        ll.append(x)
    loop = ll

v2i = [-1 for _ in range(N)]
for i, v in enumerate(loop):
    v2i[v] = i

i = 0
vs = set()
ss = set()
lnum = len(loop)
ll = []
while True:
    v = loop[i]
    if i in vs:
        f = False
        loop = []
        for x in ll:
            if v == x:
                f = True
            if f:
                loop.append(x)
        break

    m = 0
#    print(v, d[v], v2i, ss, vs)
    for u in d[v]:
        if v2i[u] == -1:
            continue
        if v2i[u] in ss:
            continue
        if v2i[v] > v2i[u]:
            m = max(lnum - v2i[v] + v2i[u], m)
        else:
            m = max(v2i[u] - v2i[v], m)
#        print(u, m, v2i[u])
    for j in range(m-1):
        ss.add((i + j + 1) % lnum)
    vs.add(i)
    ll.append(v)
#    print(i, m, loop)
    i = (i + m) % lnum
#    print(i)

print(len(loop))
for i in loop:
    print(i+1)