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())

EIN=[0]*N
EOUT=[0]*N

EINLIST=[[] for i in range(N)]
EOUTLIST=[[] for i in range(N)]

for i in range(M):
    x,y=map(int,input().split())
    x-=1
    y-=1

    EOUT[x]+=1
    EIN[y]+=1

    EOUTLIST[x].append(y)
    EINLIST[y].append(x)

from collections import deque

Q=deque()
USE=[1]*N

for i in range(N):
    if EIN[i]==0 or EOUT[i]==0:
        Q.append(i)
        USE[i]=0

while Q:
    x=Q.pop()

    for to in EOUTLIST[x]:
        if USE[to]==0:
            continue
        EIN[to]-=1
        if EIN[to]==0:
            Q.append(to)
            USE[to]=0

    for fr in EINLIST[x]:
        if USE[fr]==0:
            continue
        EOUT[fr]-=1
        if EOUT[fr]==0:
            Q.append(fr)
            USE[fr]=0
            
def loopfind():
    for i in range(N):
        if USE[i]==1:
            break
    else:
        return []
    
    Q=deque()
    Q.append(i)
    USESET={i}
    ANS=[i]

    while True:
        for to in EOUTLIST[ANS[-1]]:
            if USE[to]==1:
                nextv=to
                break

        if nextv in USESET:
            break
        else:
            ANS.append(nextv)
            USESET.add(nextv)

    x=ANS.index(nextv)
    return ANS[x:]
        

def shortcut(ANS):
    #print(ANS)

    ANSSET=set(ANS)
    LEN=len(ANS)
    flag=0

    for i in range(LEN):
        for to in EOUTLIST[ANS[i]]:
            if to in ANSSET and ANS[(i+1)%LEN]!=to:
                flag=1
                x=ANS.index(to)

                #print(ANS,i,x)

                break
        if flag:
            break
    #print(flag)

    if flag:
        if x<i:
            return shortcut(ANS[x:i+1])
        else:
            return shortcut(ANS[x:]+ANS[:i+1])

    else:
        return ANS

ANS=shortcut(loopfind())
if len(ANS)==0:
    print(-1)
else:
    print(len(ANS))
    for ans in ANS:
        print(ans+1)