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
input = sys.stdin.readline        

def main():

    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
    
    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)

    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

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

main()