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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

import sys
bbn=1000000007
	
#+++++

def modinv(a,m):
	b=m
	u=1
	v=0
	
	while b > 0:
		t = a //b
		a = a - (t * b)
		a,b = b,a
		u = u - (t * v)
		u,v=v,u
	
	u = u % m
	if u < 0:
		u+=m
	return u

def gcd(a,b):
	while b!= 0:
		a,b=b,a%b
		
	return a
		
def main():
	n = int(input())
	al = list(map(int, input().split()))
	
	#saisyoukoubausuu
	ss=1
	for v in al:
		ss = ss*v//gcd(ss,v) 
		#ss %= bbn
	
	ret=0
	for v in al:
		ret+=(ss * modinv(v,bbn))
		ret%=bbn
		
	
	print(ret)
	
	
#+++++
isTest=False

def pa(v):
	if isTest:
		print(v)

if __name__ == "__main__":
	if sys.platform =='ios':
		sys.stdin=open('inputFile.txt')
		isTest=True
	else:
		pass
		#input = sys.stdin.readline
			
	ret = main()
	if ret is not None:
		print(ret)