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
sys.setrecursionlimit(10**5)

N, M = map(int, input().split())
G = [[] for _ in range(N+1)]
for _ in range(M):
    A, B = map(int, input().split())
    G[A].append(B)

def dfs(v, o):
    for c in G[v]:
        if c == o:
            return [v]
    for c in G[v]:
        if visited[c]:
            continue
        visited[c] = True
        ret = dfs(c, o)
        if ret:
            return [v] + ret

for v in range(1, N+1):
    visited = [False] * (N+1)
    cur = dfs(v, v)
    if cur:
        break
else:
    print(-1)
    exit()

while True:
    cur_set = set(cur)
    unused = None
    for i in range(len(cur)):
        u, v = cur[i], cur[(i+1) % len(cur)]
        for c in G[u]:
            if c == v:
                continue
            elif c in cur_set:
                unused = (i, cur.index(c))
                break

    if not unused:
        break
    else:
        t, s = unused
        nxt = []
        i = s
        while i != t:
            nxt.append(cur[i])
            i = (i + 1) % len(cur)
        nxt.append(cur[t])
        cur = nxt

print(len(cur))
print(*cur, sep='\n')