Problem:
Score : 600 points

Problem Statement

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.

Notes

For a directed graph G = (V, E), we call a directed graph G' = (V', E') satisfying the following conditions an induced subgraph of G:

V' is a (non-empty) subset of V.

E' is the set of all the edges in E that have both endpoints in V'.

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.

Sample Input 1

4 5
1 2
2 3
2 4
4 1
4 3

Sample Output 1

3
1
2
4

The induced subgraph of G whose vertex set is \{1, 2, 4\} has the edge set \{(1, 2), (2, 4), (4, 1)\}. The in-degree and out-degree of every vertex in this graph are both 1.

Sample Input 2

4 5
1 2
2 3
2 4
1 4
4 3

Sample Output 2

-1

There is no induced subgraph of G that satisfies the condition.

Sample Input 3

6 9
1 2
2 3
3 4
4 5
5 6
5 1
5 2
6 1
6 2

Sample Output 3

4
2
3
4
5

Solution in C (GCC 5.4.1) (judge verdict: Runtime Error)

#include <stdio.h>
#include <stdlib.h>

// Max verticles
#define N 1000
// Max edges
#define M 2000

// Num of verticles
static int n;
// Num of edges
static int m;

struct edge {
    int start;
    int end;
};

static struct edge edges[M];

static struct edge el[M];
static int el_len = 0;

int find_first_closed_graph(int start) {
    // printf("start=%d\n", start);
    for (int i = 0; i < m; i++) {
        if (edges[i].start == start) {
            // printf("  %d -> %d\n", edges[i].start, edges[i].end);
            el[el_len] = edges[i];
            el_len++;

            // Found closed graph
            if (el_len > 1) {
                if (el[el_len-1].end == el[0].start) {
                    return 1;
                }
            }

            if (find_first_closed_graph(el[el_len-1].end)) {
                return 1;
            }
            el_len--;
        }
    }

    // Not found closed graph
    // printf("end\n");
    return 0;
}

/*
 * Return an index of the edgd, otherwise -1.
 */
int find_edge_not_used_in_graph() {
    for (int i = 0; i < el_len; i++) {
        for (int j = 0; j < m; j++) {
            if (edges[j].start == el[i].start) {
                for (int k = 0; k < el_len; k++) {
                    if ((k != i) && (edges[j].end == el[k].end)) {
                        return j;
                    }
                }
            }
        }
    }

    return -1;
}

void recreate_closed_graph(int ind) {
    struct edge e = edges[ind];
    int i, j;

    for (i = 0; i < el_len; i++) {
        if (edges[i].start == e.start) {
            break;
        }
    }
    if (i >= el_len) {
        return;
    }

    for (j = 0; j < el_len; j++) {
        if (edges[j].end == e.end) {
            break;
        }
    }
    if (j >= el_len) {
        return;
    }

    // printf("%d, %d\n", i, j);

    if (j > i) {
        el[i] = e;
        for (int k = 0; k < el_len - 1 - j; k++) {
            el[i+1+k] = el[j+1+k];
        }
        el_len -= (j - i);
    } else {
        el[i] = e;
        for (int k = j+1; k <= i; k++) {
            el[k-(j+1)] = el[k];
        }
        el_len = i - j;
    }
}

int main(void) {
    scanf("%d %d", &n, &m);

    for (int i = 0; i < m; i++) {
        int a, b;
        scanf("%d %d", &a, &b);
        edges[i].start = a;
        edges[i].end = b;
    }

    if (find_first_closed_graph(1)) {
        for (;;) {
            // for (int i = 0; i < el_len; i++) {
            //     printf("%d -> %d\n", el[i].start, el[i].end);
            // }
            // printf("\n");

            int ind = find_edge_not_used_in_graph();
            if (ind >= 0) {
                // printf("use %d -> %d\n", edges[ind].start, edges[ind].end);
                recreate_closed_graph(ind);
            } else {
                printf("%d\n", el_len);
                for (int i = 0; i < el_len; i++) {
                    printf("%d\n", el[i].start);
                    // printf("%d -> %d\n", el[i].start, el[i].end);
                }
                break;
            }
        }
    } else {
        printf("%d\n", -1);
    }

    return 0;
}