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 Python (3.4.3) (judge verdict: Time Limit Exceeded)



def gcd_core(a, b):
    while b != 0:
        a, b = b, a % b
    return a

def gcd(arr):
    g = gcd_core(arr[0], arr[1])
    for i in range(2, len(arr)):
        g = gcd_core(g, arr[i])
    return g


def lcm_core(a,b):
    g = gcd_core(a,b)
    return (a*b)//g

def lcm(arr):
    if len(arr) == 1:
        return arr[0]
    else:
        newl = []
        ind = 0
        while True:
            if ind + 1 < len(arr):
                newl.append(lcm_core(arr[ind],arr[ind+1]))
                ind += 2
            else:
                newl.append(arr[ind])
                ind += 1
            if ind >= len(arr):
                break
        return lcm(newl)


n = int(input())

if n == 1:
    print(1)
else:
    arr = list(map(int,input().split()))
    l = lcm(arr)
    m = 10**9+7
    l,mcnt = l%m,l//m
    ans = 0
    for i in range(n):
        temp1 = l // arr[i] + (m // arr[i]) * mcnt
        temp2 = l % arr[i] + (m % arr[i]) * mcnt
        temp2 = temp2 // arr[i]
        ans += temp1 + temp2
        ans %= m
    ans %= m
    print(ans)