Problem:
Score : 500 points

Problem Statement

Given are N positive integers A_1,...,A_N.

Consider positive integers B_1, ..., B_N that satisfy the following condition.

Condition: For any i, j such that 1 \leq i < j \leq N, A_i B_i = A_j B_j holds.

Find the minimum possible value of B_1 + ... + B_N for such B_1,...,B_N.

Since the answer can be enormous, print the sum modulo (10^9 +7).

Constraints

1 \leq N \leq 10^4

1 \leq A_i \leq 10^6

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 ... A_N

Output

Print the minimum possible value of B_1 + ... + B_N for B_1,...,B_N that satisfy the condition, modulo (10^9 +7).

Sample Input 1

3
2 3 4

Sample Output 1

13

Let B_1=6, B_2=4, and B_3=3, and the condition will be satisfied.

Sample Input 2

5
12 12 12 12 12

Sample Output 2

5

We can let all B_i be 1.

Sample Input 3

3
1000000 999999 999998

Sample Output 3

996989508

Print the sum modulo (10^9+7).

Solution in Kotlin (1.0.0) (judge verdict: Wrong Answer)

fun main(args: Array<String>) {
    abc152e()
}

fun abc152e() {
    val n = readLine()!!.toInt()
    val aList = readLine()!!.split(' ').map { it.toLong() }

    val lcm = aList.reduce { acc, l -> lcm(acc, l) }

    val bList = aList.map { lcm / it }

    var answer = Mint(0L)

    for (b in bList) {
        answer += b
    }

    println(answer)
}

private fun lcm(a: Long, b: Long): Long {
    return a / gcd(a, b) * b
}

private tailrec fun gcd(a: Long, b: Long): Long {
    return if (b == 0L) a else gcd(b, a % b)
}

private const val MOD = (1e9 + 7).toLong()

private class Mint(value: Long) {
    val value = if (value < 0) (value % MOD) + MOD else value % MOD

    operator fun unaryPlus() = this
    operator fun unaryMinus() = Mint(MOD - this.value)
    operator fun inc() = this.plus(1)
    operator fun dec() = this.minus(1)
    operator fun plus(other: Long) = Mint(this.value + other)
    operator fun plus(other: Mint) = this.plus(other.value)
    operator fun minus(other: Long) = Mint(this.value - other)
    operator fun minus(other: Mint) = this.plus(-other)
    operator fun times(other: Long) = Mint(this.value * other)
    operator fun times(other: Mint) = this.times(other.value)
    operator fun div(other: Long) = Mint(modPow(other, MOD - 2, MOD))
    operator fun div(other: Mint) = this.div(other.value)
    override fun toString(): String {
        return this.value.toString()
    }

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

        other as Mint

        if (value != other.value) return false

        return true
    }

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

    @Suppress("SameParameterValue")
    companion object Mod {
        private fun modPow(n: Long, p: Long, m: Long): Long {
            var x = n
            var y = p
            var result = 1L
            x %= m
            while (y > 0) {
                if (y % 2 == 1L)
                    result = (result * x) % m
                y = y shr 1
                x = (x * x) % m
            }
            return result
        }
    }
}