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: Time Limit Exceeded)

val MaxNodes = 1000
val NewState = 1
val ActiveState = 2
val FinishState = 3
val nodeStatus = IntArray(MaxNodes, { NewState })
val edges = Array(MaxNodes) { mutableSetOf<Int>() }

fun main(args: Array<String>) {
    val (N, M) = readInputLine().split(" ").map { it.toInt() }

    for (i in 1..M) {
        val (A, B) = readInputLine().split(" ").map { it.toInt()  - 1 }
        edges[A].add(B)
    }

    var ret = existsCycle()

    if (!ret.first) {
        println(-1)
        return
    }
    
    ret.third.reverse()
    
    while (true) {
        // 次数チェック
        var ok = true
        var unUsedStart = -1
        var unUsedEnd = -1
        for (n in ret.third) {
            val intersect = ret.third.intersect(edges[n])
            if (intersect.size != 1) {
                ok = false
                val nIndex = ret.third.indexOf(n)
                for (e in intersect) {
                    if ((nIndex + 1) % ret.third.size != ret.third.indexOf(e)) {
                        unUsedStart = n
                        unUsedEnd = e
                        break
                    }
                }
                break
            }
        }
        if (ok) {
            println(ret.third.size)
            for (n in ret.third) {
                println(n + 1)
            }
            return
        }

        // 余分なノードを除去
        val visited = mutableListOf(unUsedEnd)
        var current = ret.third.intersect(edges[unUsedEnd]).first()
        while (current != unUsedStart) {
            visited.add(current)
            current = ret.third.intersect(edges[current]).first()
        }
        visited.add(unUsedStart)
        ret = ret.copy(third = visited)
    }
}

fun readInputLine(): String {
    return readLine()!!
}

fun existsCycle(): Triple<Boolean, Boolean, MutableList<Int>> {
    for (v in 0 until MaxNodes) {
        if (nodeStatus[v] == NewState) {
            val ret = existsCycleSub(v)
            if (ret.first) {
                return ret
            }
        }
    }
 
    return Triple(false, false, mutableListOf<Int>())
}
 
fun existsCycleSub(source: Int): Triple<Boolean, Boolean, MutableList<Int>> {
    nodeStatus[source] = ActiveState
    
    for (e in edges[source]) {
        if (nodeStatus[e] == ActiveState) {
            return Triple(true, false, mutableListOf(e, source))
        } else if (nodeStatus[e] == NewState) {
            val ret = existsCycleSub(e)
            if (ret.first) {
                if (ret.second) {
                    return ret
                }
                if (ret.third.contains(source)) {
                    return ret.copy(second = true)
                }
                ret.third.add(source)
                return ret
            }
        }
    }
    nodeStatus[source] = FinishState

    return Triple(false, false, mutableListOf<Int>())
}