Problem:
Score : 1000 points

Problem Statement

How many infinite sequences a_1, a_2, ... consisting of {{1, ... ,n}} satisfy the following conditions?

The n-th and subsequent elements are all equal. That is, if n \leq i,j, a_i = a_j.

For every integer i, the a_i elements immediately following the i-th element are all equal. That is, if i < j < k\leq i+a_i, a_j = a_k.

Find the count modulo 10^9+7.

Constraints

1 \leq n \leq 10^6

Input

Input is given from Standard Input in the following format:

n

Output

Print how many sequences satisfy the conditions, modulo 10^9+7.

Sample Input 1

2

Sample Output 1

4

The four sequences that satisfy the conditions are:

1, 1, 1, ...

1, 2, 2, ...

2, 1, 1, ...

2, 2, 2, ...

Sample Input 2

654321

Sample Output 2

968545283

Solution in Kotlin (1.3.71) (judge verdict: Accepted)

import java.io.BufferedReader
import java.io.InputStream
import java.io.InputStreamReader
import java.io.PrintWriter
import java.lang.Exception
import java.util.*

// ModInt
// region
class ModInt(x: Long) {

    companion object {
        const val MOD = 1000000007L
        //const val MOD = 998244353L
    }

    val x = (x % MOD + MOD) % MOD

    operator fun plus(other: ModInt): ModInt {
        return ModInt(x + other.x)
    }

    operator fun minus(other: ModInt): ModInt {
        return ModInt(x - other.x)
    }

    operator fun times(other: ModInt): ModInt {
        return ModInt(x * other.x)
    }

    operator fun div(other: ModInt): ModInt {
        return this * other.inv()
    }

    fun pow(exp: Long): ModInt {
        if (exp == 0L) return ModInt(1L)
        var a = pow(exp shr 1)
        a *= a
        if (exp and 1L == 0L) return a
        return this * a
    }

    fun inv(): ModInt {
        return this.pow(MOD - 2)
    }

    override fun equals(other: Any?): Boolean {
        if (this === other) return true
        if (javaClass != other?.javaClass) return false

        other as ModInt

        if (x != other.x) return false

        return true
    }

    override fun hashCode(): Int {
        return x.hashCode()
    }

    override fun toString(): String {
        return "$x"
    }

}

val fac = mutableListOf<ModInt>()
val invfac = mutableListOf<ModInt>()

fun fact(n: Long, b: Boolean): ModInt {
    if (fac.count() == 0) {
        fac.add(ModInt(1))
        invfac.add(ModInt(1))
    }
    while (fac.count() <= n) {
        fac.add(fac.last() * ModInt(fac.count().toLong()))
        invfac.add(fac.last().inv())
    }
    return if (b) {
        fac[n.toInt()]
    } else {
        invfac[n.toInt()]
    }
}

fun comb(n: Long, k: Long): ModInt {
    return fact(n, true) * fact(k, false) * fact(n - k, false)
}

fun comb2(n: Long, k: Long): ModInt {
    var ans = ModInt(1)
    for (i in 0 until k) {
        ans = ans * ModInt(n - i) / ModInt(k - i)
    }
    return ans
}
// endregion

fun PrintWriter.solve(sc: FastScanner) {
    val n = sc.nextInt()
    val dp = Array(n + 2) { ModInt(0) }
    dp[1] = ModInt(n.toLong())
    dp[2] = dp[1].pow(2)
    var sum = dp[2] + ModInt(n - 1L)
    for (i in 3..n) {
        dp[i] = ModInt(n - 1L).pow(2) + sum
        sum += dp[i] - dp[i-1] + dp[i-2] - ModInt(1)
    }
    println(dp[n])
}

fun main() {
    val writer = PrintWriter(System.out, false)
    writer.solve(FastScanner(System.`in`))
    writer.flush()
}

class FastScanner(s: InputStream) {
    private var st = StringTokenizer("")
    private val br = BufferedReader(InputStreamReader(s))

    fun next(): String {
        while (!st.hasMoreTokens()) st = StringTokenizer(br.readLine())

        return st.nextToken()
    }

    fun nextInt() = next().toInt()
    fun nextLong() = next().toLong()
    fun nextLine() = br.readLine()
    fun nextDouble() = next().toDouble()
    fun ready() = br.ready()
}