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)

import java.util.*

var g = Array(0){IntArray(0)}
var rg = Array(0){IntArray(0)}

fun main(args: Array<String>) = IO().exec {
    val n = int()
    val m = int()
    val a = IntArray(m)
    val b = IntArray(m)
    for (i in m) {
        a[i] = int()-1
        b[i] = int()-1
    }
    g = mkDGraph(n, a, b)
    rg = mkDGraph(n, b, a)
    state = IntArray(n)
    for (v in n) {
        if (state[v] == 0) {
            val ret = dfs(v)
            if (ret != null) {
                ret.reverse()
                println(ret.size)
                for (r in ret) println(r+1)
                return@exec
            }
        }
    }

    println(-1)
}

var state = IntArray(0)

fun dfs(v: Int): MutableList<Int>? {
    state[v] = 1
    var r: MutableList<Int>? = null
    for (nv in g[v]) {
        if (state[nv] == 1) {
            val ret = mutableListOf(v)
            var c = v
            while (true) {
                if (c == nv) break
                for (p in rg[c]) {
                    if (state[p] == 1) {
                        c = p
                        ret.add(p)
                        break
                    }
                }
            }
            return ret
        }
        if (state[nv] == 0) {
            val ret = dfs(nv)
            if (ret != null && (r != null && ret.size < r.size) || r == null)
                r = ret
        }
    }
    state[v] = 2
    return r
}

fun mkDGraph(n: Int, from: IntArray, to: IntArray): Array<IntArray> {
    val ret: Array<IntArray> = Array(n){IntArray(0)}
    val cnt = IntArray(n)
    for (f in from) cnt[f]++
    for (i in 0 until n) ret[i] = IntArray(cnt[i])
    for (i in from.indices)
        ret[from[i]][--cnt[from[i]]] = to[i]
    return ret
}

// region template
operator fun Int.iterator() = 0.until(this).iterator()

class IO {
    val printable = 33..126
    val buffer = ByteArray(1024)
    var ptr = 0
    var buflen = 0
    val out = java.io.PrintWriter(System.out)
    fun hasNextByte(): Boolean = if (ptr < buflen) true else {
        ptr = 0
        buflen = System.`in`.read(buffer)
        buflen > 0
    }

    fun readByte(): Byte = if (hasNextByte()) buffer[ptr++] else -1
    fun hasNext(): Boolean {
        while (hasNextByte() && buffer[ptr] !in printable) ptr++
        return hasNextByte()
    }

    fun string(): String {
        if (!hasNext()) throw java.util.NoSuchElementException()
        val sb = StringBuilder()
        var b = readByte()
        while (b in printable) {
            sb.appendCodePoint(b.toInt())
            b = readByte()
        }
        return sb.toString()
    }

    fun long(): Long {
        if (!hasNext()) throw java.util.NoSuchElementException()
        var n = 0L
        var minus = false
        var b = readByte()
        if (b == '-'.toByte()) {
            minus = true
            b = readByte()
        }
        if (b !in '0'.toByte()..'9'.toByte()) {
            throw NumberFormatException()
        }
        while (true) {
            if (b in '0'.toByte()..'9'.toByte()) {
                n *= 10
                n += b - '0'.toByte()
            } else if (b == (-1).toByte() || b !in printable) {
                return if (minus) -n else n
            } else {
                throw NumberFormatException()
            }
            b = readByte()
        }
    }

    fun int(): Int {
        val nl = long()
        if (nl !in Integer.MIN_VALUE..Integer.MAX_VALUE) throw NumberFormatException()
        return nl.toInt()
    }

    fun double(): Double = string().toDouble()
    fun print(obj: Any) = out.print(obj)
    fun print(i: Int) = out.print(i)
    fun print(l: Long) = out.print(l)
    fun println(obj: Any) = out.println(obj)
    fun println(i: Int) = out.println(i)
    fun println(l: Long) = out.println(l)
    inline fun exec(block: IO.() -> Unit) {
        block()
        out.flush()
    }

    inline fun println(block: IO.() -> Any) {
        println(block())
        out.flush()
    }
}
// endregion