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 JAVA):

Solution:
import java.io.*;
import java.util.*;

@SuppressWarnings("unused")
public class Main {
    private FastScanner in = new FastScanner(System.in);
    private PrintWriter out = new PrintWriter(System.out);
    final int MOD = (int)1e9+7;
    long ceil(long a, long b){return (a + b - 1) / b;}

    void solve() throws Exception{
        int N = in.nextInt(), M = in.nextInt();
        ArrayList<ArrayList<Integer>> G = new ArrayList<>();
        for(int i = 0; i < N; i++) G.add(new ArrayList<>());
        for(int i = 0; i < M; i++){
            int A = in.nextInt()-1, B = in.nextInt()-1;
            G.get(A).add(B);
        }

        int cost = Integer.MAX_VALUE / 2;
        ArrayList<Integer> ans = new ArrayList<>();
        for(int s = 0; s < N; s++){
            int[] dist = new int[N];
            Arrays.fill(dist, Integer.MAX_VALUE / 2);
            int[] from = new int[N];
            Arrays.fill(from, -1);
            ArrayDeque<Integer> queue = new ArrayDeque<Integer>();
            queue.addLast(s);
            dist[s] = 0;

            while(!queue.isEmpty()){
                int v = queue.removeFirst();
                for(int next : G.get(v)){
                    if(dist[next] > dist[v] + 1){
                        dist[next] = dist[v] + 1;
                        from[next] = v;
                        queue.addLast(next);
                    }
                }
                if(v == s && dist[v] == 0){
                    dist[v] = Integer.MAX_VALUE / 2;
                }
            }

            if(cost > dist[s]){
                cost = dist[s];
                ans.clear();
                int now = s;
                for(int i = 0; i < dist[s]; i++){
                    ans.add(now);
                    now = from[now];
                }
            }
        }

        if(cost == Integer.MAX_VALUE / 2){
            out.println("-1");
        }else{
            out.println(cost);
            for(int i = ans.size()-1; i >= 0; i--) out.println((ans.get(i)+1));
        }
    }

    //end solve

    public static void main(String[] args) throws Exception {
        new Main().m();
    }

    private void m() throws Exception {
        solve();
        out.flush();
    }

    static class FastScanner {
        Reader input;

        FastScanner() {this(System.in);}
        FastScanner(InputStream stream) {this.input = new BufferedReader(new InputStreamReader(stream));}

        int nextInt() {return (int) nextLong();}

        long nextLong() {
            try {
                int sign = 1;
                int b = input.read();
                while ((b < '0' || '9' < b) && b != '-' && b != '+') {
                    b = input.read();
                }
                if (b == '-') {
                    sign = -1;
                    b = input.read();
                } else if (b == '+') {
                    b = input.read();
                }
                long ret = b - '0';
                while (true) {
                    b = input.read();
                    if (b < '0' || '9' < b) return ret * sign;
                    ret *= 10;
                    ret += b - '0';
                }
            } catch (IOException e) {
                e.printStackTrace();
                return -1;
            }
        }

        double nextDouble() {
            try {
                double sign = 1;
                int b = input.read();
                while ((b < '0' || '9' < b) && b != '-' && b != '+') {
                    b = input.read();
                }
                if (b == '-') {
                    sign = -1;
                    b = input.read();
                } else if (b == '+') {
                    b = input.read();
                }
                double ret = b - '0';
                while (true) {
                    b = input.read();
                    if (b < '0' || '9' < b) break;
                    ret *= 10;
                    ret += b - '0';
                }
                if (b != '.') return sign * ret;
                double div = 1;
                b = input.read();
                while ('0' <= b && b <= '9') {
                    ret *= 10;
                    ret += b - '0';
                    div *= 10;
                    b = input.read();
                }
                return sign * ret / div;
            } catch (IOException e) {
                e.printStackTrace();
                return Double.NaN;
            }
        }

        char nextChar() {
            try {
                int b = input.read();
                while (Character.isWhitespace(b)) {
                    b = input.read();
                }
                return (char) b;
            } catch (IOException e) {
                e.printStackTrace();
                return 0;
            }
        }

        String nextStr() {
            try {
                StringBuilder sb = new StringBuilder();
                int b = input.read();
                while (Character.isWhitespace(b)) {
                    b = input.read();
                }
                while (b != -1 && !Character.isWhitespace(b)) {
                    sb.append((char) b);
                    b = input.read();
                }
                return sb.toString();
            } catch (IOException e) {
                e.printStackTrace();
                return "";
            }
        }

        public int[] nextIntArray(int n) {
            int[] res = new int[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextInt();
            }
            return res;
        }

        public int[] nextIntArrayDec(int n) {
            int[] res = new int[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextInt() - 1;
            }
            return res;
        }

        public int[] nextIntArray1Index(int n) {
            int[] res = new int[n + 1];
            for (int i = 0; i < n; i++) {
                res[i + 1] = nextInt();
            }
            return res;
        }

        public long[] nextLongArray(int n) {
            long[] res = new long[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextLong();
            }
            return res;
        }

        public long[] nextLongArrayDec(int n) {
            long[] res = new long[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextLong() - 1;
            }
            return res;
        }

        public long[] nextLongArray1Index(int n) {
            long[] res = new long[n + 1];
            for (int i = 0; i < n; i++) {
                res[i + 1] = nextLong();
            }
            return res;
        }

        public double[] nextDoubleArray(int n) {
            double[] res = new double[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextDouble();
            }
            return res;
        }

        public Long[] nextWrapperLongArray(int n) {
            Long[] res = new Long[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextLong();
            }
            return res;
        }

        public Long[] nextWrapperLongArrayDec(int n) {
            Long[] res = new Long[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextLong() - 1;
            }
            return res;
        }

        public Long[] nextWrapperLongArray1Index(int n) {
            Long[] res = new Long[n + 1];
            for (int i = 0; i < n; i++) {
                res[i + 1] = nextLong();
            }
            return res;
        }
    }
}