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:
import sys
input = sys.stdin.readline

n,m = map(int,input().split())

edge = [[] for _ in [0]*n]
back = [[] for _ in [0]*n]

for _ in [0]*m:
    a,b = map(int,input().split())
    edge[a-1].append(b-1)
    back[b-1].append(a-1)


res = [None]*(n+1)

for end in range(n):
    for start in edge[end]:
        cost = [-1]*n
        cost[start] = 0
        new = [start]
        tank = []
        judge = True

        while len(new) > 0 and judge:
            tank = []
            for fr in new:
                for go in edge[fr]:
                    if cost[go] < 0:
                        cost[go] = cost[fr] + 1
                        tank.append(go)
                        if go == end:
                            judge = False
            new = tank

        
        if cost[end] >= 0 and cost[end] < len(res):
            p = end
            res = [p+1]
            while p != start:
                for e in back[p]:
                    if cost[p] == cost[e]+1:
                        p = e
                        res.append(p+1)
                        break
if res[0] == None:
    print(-1)
else:                      
    print(len(res))
    for e in res:
        print(e)