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 Java7 (OpenJDK 1.7.0) (judge verdict: Runtime Error)

import java.util.*;
public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		// 整数の入力
		int a = sc.nextInt();
      int[] ary = new int[a];
      int[] lc = new int[a];
      int max=0;
      for (int i=0;i < a;i++){
        ary[i]=sc.nextInt();
      }
      max=ary[0];
      for (int i=1;i < a;i++){
        max=lcm(max,ary[i]);
      }
      int ans = 0;

      for (int i=0;i < a;i++){
        ans +=(max/ary[i]);
      }
      System.out.println(ans % (1000000000+7));
	}
  private static int lcm(int m, int n){
    return m * n / gcd(m,n);
  }
  private static int gcd(int m,int n){
    if(m<n) return gcd(n,m);
    if(n==0) return m;
    return gcd(n,m%n);
  }
}