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
from collections import deque
from collections import defaultdict
import copy

n, m = map(int, sys.stdin.readline().split())
adj = [[] for _ in range(n+1)]
radj = [[] for _ in range(n+1)]
for _ in range(m):
    a, b = map(int, sys.stdin.readline().split())
    adj[a].append(b)
    radj[b]


def searchRoute(i):
    global adj
    nexts = deque()
    route = [i]
    visited = set()
    result = []
    for x in adj[i]:
        if x < i:
            continue
        nroute = copy.copy(route)
        nexts.append((x, nroute))
    while len(nexts) > 0:
        error = False
        found = False
        x, xroute = nexts.popleft()
        xroute.append(x)
        visited.add(x)
        for y in adj[x]:
            if y < i:
                continue
            if y == i:
                found = True
                break
            if y in visited:
                break
            yroute = copy.copy(xroute)
            nexts.append((y, yroute))
        if found:
            result = xroute
            break
    return result

heiro = []
for i in range(1, n+1):
    res = searchRoute(i)
    if len(res) > 0:
        heiro = res
        break

if len(heiro) == 0:
    print(-1)
    exit()
while True:
    visited = set()
    bp = [-1, -1]
    rt = defaultdict(int)
    for i in range(len(heiro)):
        visited.add(heiro[i])
        rt[heiro[i]] = i
        for j in adj[heiro[i]]:
            if j in visited and not (i == len(heiro) - 1 and j == heiro[0]):
                bp = [i, rt[j]]
                break
        if bp[0] != -1:
            break
    if bp[0] == -1:
        print(len(heiro))
        for i in heiro:
            print(i)
        exit()
    heiro = heiro[bp[1]:bp[0]+1]