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 = 0L

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

    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()