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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <math.h>

long gcd(long a, long b){
    long temp;

    if(a<b){
        temp=b;
        b=a;
        a=temp;
    }

    while(b!=0){
        temp=b;
        b=a%b;
        a=temp;
    }
    return a;
}

long gongbeishu(long a,long b){
    return a*b/gcd(a,b);
}

long shuzugongbeishu(int a[],int len){
    long temp[len];
	int i;
    for(i=0;i<len;i++){
        temp[i]=a[i];
    }
	
    for(i=1;i<len;i++){
        temp[i]=gongbeishu(temp[i-1],temp[i]);
		//printf("%d",temp[i]);
    }
    return temp[len-1];
}

int main(){
    int N,i;
	long int cnt=0,gongbeishu;
    scanf("%d",&N);
    int A[N];
    for(i=0;i<N;i++){
        scanf("%d",&A[i]);
    }

	gongbeishu=shuzugongbeishu(A,N);
	
	//printf("%ld\n",gongbeishu);

	for(i=0;i<N;i++){
		cnt+=gongbeishu/A[i];
	}

	printf("%ld\n",cnt%(int)(pow(10,9)+7));

    return 0;
}