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 Kotlin (1.0.0) (judge verdict: Runtime Error)

fun main(args: Array<String>) {
    val (n, m) = readLine()!!.split(" ").map(String::toInt)
    val graph = mutableMapOf<Int, Set<Int>>()

    repeat(n) {
        graph[it] = setOf()
    }
    repeat(m) {
        val (n1, n2) = readLine()!!.split(" ").map(String::toInt)
        graph[n1] = graph.getOrDefault(n1, setOf()) + n2
    }

    var (loopGraph, path) = findLoop(graph)

    if (loopGraph.isEmpty()) {
        println(-1)
        return
    }

    val pureLoop = loopGraph.getPureLoop()
    println(pureLoop.size)
    pureLoop.forEach{ println(it)}
}

fun findLoop(g: MutableMap<Int, Set<Int>>): Pair<MutableMap<Int, Set<Int>>, List<Int>> {
    val graph = g

    fun run(node: Int, done: List<Int> = listOf()): List<Int> {
        when {
            done.contains(node) -> return done
            graph.getOrDefault(node, setOf()).isEmpty() -> return done + node
                else -> {
                for (n in graph.getOrDefault(node, setOf())) {
                    val path = run(n, done + node)
                    if (graph.getOrDefault(path.last(), setOf()).contains(path.first())) return path
                }

                return done + node
            }
        }
    }

    while (graph.keys.isNotEmpty()) {
        val origin = graph.keys.first()
        val path = run(origin)

        if (graph.getOrDefault(path.last(), setOf()).contains(origin)) {
            graph.del(graph.keys - path)
            return Pair(graph, path)
        } else {
            graph.del(path)
        }
    }

    return Pair(mutableMapOf(), listOf())
}

fun Map<Int, Set<Int>>.isPure(): Boolean {
    val hasOneDst = this.values.all { it.size == 1 }
    val hasOneOgn = this.keys.all { n ->
        this.filter { it.value.contains(n) }.size == 1
    }

    return hasOneDst && hasOneOgn
}

fun MutableMap<Int, Set<Int>>.del(node: Int) {
    this.remove(node)
    this.keys.forEach { this[it] = this[it]!! - node }
}

fun MutableMap<Int, Set<Int>>.del(nodes: Iterable<Int>) {
    nodes.forEach { this.del(it) }
}

fun MutableMap<Int, Set<Int>>.getPureLoop(): List<Int> {
    fun getPath(node: Int, done: List<Int> = listOf()): List<Int> {
        return when {
            done.contains(node) -> done
            else -> getPath(this[node]!!.first(), done + node)
        }
    }

    var path = getPath(this.keys.first())
    this.del(this.keys - path)

    while (!isPure()) {
        val ogn = this.filter { it.value.size != 1 }.keys.first()
        val ognIndex = path.indexOf(ogn)
        val dst = (this[ogn]!! - path[(ognIndex + 1) % path.size]).first()
        val dstIndex = path.indexOf(dst)

        val idx1 = min(ognIndex, dstIndex)
        val idx2 = max(ognIndex, dstIndex)
        path = path.slice(idx1..idx2)
        this.del(this.keys - path)
    }

    return path
}

fun <K, V> Map<K, V>.getOrDefault(key: K, default: V): V = this[key] ?: default
fun max(i: Int, j: Int): Int {
    return if (i < j) j else i
}

fun min(i: Int, j: Int): Int {
    return if (i < j) i else j
}