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: Wrong Answer)

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

static int abs2(int a, int b) {
    return a < b ? b - a : a - b;
}

// 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 *map[N+1][N+1]; // map[b][a] points to a edge a -> b

static bool visited[N+1];

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

bool 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
            for (int j = 0; j < el_len-1; j++) {
                if (el[j]->start == el[el_len-1]->end) {
                    el_len -= j;
                    for (int k = 0; k < el_len; k++) {
                        el[k] = el[k+j];
                    }
                    return 1;
                }
            }

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

    visited[start] = true;

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

struct edge *find_edge_not_used_in_graph() {
    for (int i = 0; i < el_len; i++) {
        for (int j = 0; j < el_len; j++) {
            if (abs2(i, j) <= 1) continue;
            if ((i == 0 && j == el_len-1) || (i == el_len-1 && j == 0)) continue;

            if (map[el[j]->start][el[i]->start] != NULL) {
                return map[el[j]->start][el[i]->start];
            }
        }
    }

    return NULL;
}

void recreate_closed_graph(struct edge *ep) {
    int i, j;

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

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

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

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

int main(void) {
    struct edge *ep;
    bool has_closed_graph;

    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;
        map[b][a] = &edges[i];
    }

    for (int i = 1; i <= n; i++) {
        if (!visited[i]) {
            has_closed_graph = find_first_closed_graph(i);
            if (has_closed_graph) {
                break;
            }
        }
    }

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

        //     ep = find_edge_not_used_in_graph();
        //     if (ep != NULL) {
        //         // printf("use %d -> %d\n", edges[ind].start, edges[ind].end);
        //         recreate_closed_graph(ep);
        //     } 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;
        //     }
        // }
        printf("%d\n", 1);
    } else {
        printf("%d\n", -1);
    }

    return 0;
}