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 = map(int, input().split())
ab = [list(map(int, input().split())) for _ in range(m)]

from collections import defaultdict, deque
g = defaultdict(list)
for a, b in ab:
    g[a-1].append(b - 1)

ans = None
for start in range(n):
    visited = [0] * n
    visited[start] = 1
    q = deque([start])
    prev = [None] * n

    f = False
    while q:
        cur = q.popleft()

        for target in g[cur]:
            if visited[target] == 0:
                visited[target] = 1
                q.append(target)
                prev[target] = cur

            if target == start:
                f = True
                break

        if f:
            break

    if f:
        loop = [target]
        while cur != None:
            loop.append(cur)
            cur = prev[cur]

        loop = loop[::-1]
        v = set(loop)

        f2 = True
        for i in range(len(loop) - 1):
            a, b = loop[i], loop[i+1]

            for target in g[a]:
                if target in v and target != b:
                    f2 = False
                    break

            if f2 == False:
                break

        if f2:
            ans = loop[:-1]
            break

if ans == None:
    print(-1)
else:
    print(len(ans))
    for _ans in ans:
        print(_ans + 1)