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:
def search(N, M, adj):
    reachable = [[set() for i in range(N)] for _ in range(N)]
    reachable[0] = adj
    start = -1
    for m in range(1, N):
        prev = reachable[m-1]
        cur = reachable[m]
        #        for i in range(N):
        #            cur[i] = set(prev[i])
        for i in range(N):
            for nxt in adj[i]:
                for p in prev[nxt]:
                    cur[i].add(p)
                if i in prev[nxt]:
                    return (i, reachable, m+1)
    return None


def main():
    N, M = map(int, input().split())
    adj = [set() for _ in range(N)]
    for _ in range(M):
        A, B = map(int, input().split())
        adj[A-1].add(B-1)
    result = search(N, M, adj)
    if not result:
        print(-1)
        return
    start, reachable, cnt = result
    ans = [-1] * cnt
    x = start
    for i in range(cnt):
        ans[i] = x+1
        for nxt in adj[x]:
            if start in reachable[cnt-i-2][nxt]:
                x = nxt
                break
    print(len(ans))
    for a in ans:
        print(a)


if __name__ == "__main__":
    main()