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 Ruby (2.3.3) (judge verdict: Accepted)

$mod = 10**9+7

def pow(a,b)
  if b == 1
    a
  elsif b%2 == 0
    (pow(a,b/2)**2)%$mod
  else
    (a*pow(a,b/2)**2)%$mod
  end
end

def create_fact(n)
  for i in 2..n
    $fact[i] = ($fact[i-1]*i)%$mod
  end
end

def create_fact_inv(n)
  $fact_inv[n] = pow($fact[n],$mod-2)
  n.downto(1) do |i|
    $fact_inv[i-1] = ($fact_inv[i]*i)%$mod
  end
end

def create_inv(n)
  for i in 1..n
    $inv[i] = ($fact[i-1]*$fact_inv[i])%$mod
  end
end

def init(n)
  $fact = Array.new(n+1,1)
  $fact_inv = Array.new(n+1,1)
  $inv = Array.new(n+1,0)
  create_fact(n)
  create_fact_inv(n)
  create_inv(n)
end

def combi(a,b)
  (($fact[a]*$fact_inv[b])%$mod)*$fact_inv[a-b]%$mod
end

init(1000010)
n = gets.to_i
a = gets.split.map(&:to_i)
ans = 1
a.each do |i|
    ans = ans.lcm(i)
end
ans %= $mod
c = 0
a.each do |i|
    c += $inv[i]
    c %= $mod
end
puts ans*c%$mod