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 PHP (7.4.4) (judge verdict: Wrong Answer)

<?php
define('MOD', 10 ** 9 + 7);
list($n) = ints();
$a = ints();
$x = lcmAll($a);
$ans = 0;
for ($i = 0; $i < $n; ++$i) {
    $ans += intdiv($x, $a[$i]);
    $ans %= MOD;
}
echo $ans;
function ints()
{
    return array_map('intval', explode(' ', trim(fgets(STDIN))));
}

// 最大公約数（2つ）
function gcd($m, $n)
{
    if (!$n) return $m;
    return gcd($n, $m % $n);
}

// 最大公約数（3つ以上）
function gcdAll($arr)
{
    $gcd = array_pop($arr);
    foreach ($arr as $a) {
        $gcd = gcd($gcd, $a);
    }
    return $gcd;
}

// 最小公倍数（2つ）
function lcm($m, $n)
{
    return (int) ($m / gcd($m, $n) * $n); // オーバーフローしないように先に割り算
}

// 最小公倍数（3つ以上）
function lcmAll($arr)
{
    $lcm = array_pop($arr);
    foreach ($arr as $a) {
        $lcm = lcm($lcm, $a);
    }
    return $lcm;
}