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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;
public class Main { 
    public static void main(String[] args) {
       Scanner sc=new Scanner(System.in);
       long o=0;
       int n=sc.nextInt();
       long g=1;
       long[] a=new long[n];
       for(int i=0;i<n;i++){
         a[i]=sc.nextLong();
         g=lcm(a[i],g);
       }
       g%=1000000007;
       long b=0;
       for(int i=0;i<n;i++){
         //long bi=g/a[i];
         long bi=g*modinv(a[i],1000000007)%1000000007;
         bi%=1000000007;
         b+=bi;
         b%=1000000007;
       }
       o=b%1000000007;
      //System.out.println(modinv(2,13));
      System.out.println(o);
    }
  
 static long lcm (long a, long b) {
	long temp;
	long c = a;
	c *= b;
	while((temp = a%b)!=0) {
		a = b;
		b = temp;
	}
	return (long)(c/b);
  }
  
  static long modinv(long a1,long m){
  	long b=m,u=1,v=0,a=a1;
    
    while(b>0){
    	long t=a/b;
        a-=t*b;
        long a2=a;a=b;b=a2;
        u-=t*v;
        long u2=u;u=v;v=u2;
       
    }
     u %= m; 
     if (u < 0) u += m;
     return u;
  }
}