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):
    pvs = set([v])
    path = [v]
    def _dfs(v, path):
        for u in d[v]:
            if u in pvs:
                for i, c in enumerate(path):
                    if c == u:
                        break
                return path[i+1:]  + [u]
            if u in vs:
                continue
            pvs.add(u)
            vs.add(u)
            loop = _dfs(u, path + [u])
            pvs.remove(u)
            if loop:
                return loop
        return False
    return _dfs(v, path)

def dfs_w(v):
    # dfs while版 
    pvs = set([])
    nvs = [v]
    path = []
    while True:
        if len(nvs) == 0:
            break
        v = nvs.pop()
        if v < 0:
            pvs.remove(path[-1])
            path.pop()
        else:
            path.append(v)
            pvs.add(v)
            vs.add(v)
            for u in d[v]:
                if u in pvs:
                    for i, c in enumerate(path):
                        if c == u:
                            break
                    return path[i+1:]  + [u]
                if u in vs:
                    continue
                nvs += [-v, u]
    return False

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

vs = set()
for i in range(N):
    i += 1
    if i in vs:
        continue
    vs.add(i)
    loop = dfs_w(i)
#    print(i, loop)
    if loop:
        break

if not loop:
    print(-1)
    import sys
    sys.exit()

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

nloop, pvs = [], set()
v = loop[0]
f = False
while True:
    nloop.append(v)
    pvs.add(v)
    max_i = max_i_l = -1
    for u in d[v]:
        if v2i[u] == -1:
            continue
        if v2i[v] > v2i[u] and u in pvs:
            f = True
            max_i_l = max(max_i_l, v2i[u])
        if v2i[u] > v2i[v]:
            max_i = max(max_i, v2i[u])
    if f:
        if max_i_l < 0:
            1/0
        nloop.append(loop[max_i_l])
        break
    if max_i < 0:
        1/0
    v = loop[max_i]

for i, x in enumerate(nloop):
    if x == nloop[-1]:
        break
nloop = nloop[i+1:]
print(len(nloop))
for v in nloop:
    print(v)