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: Runtime Error)

import java.util.*;
public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		// スペース区切りの整数の入力
		int b = sc.nextInt();
      int[] A=new int[b];
      int[] B=new int[b];
      int koubaisuu=1;
        for(int i=0;i<A.length;i++){
          int c=sc.nextInt();
          A[i]=c;
            koubaisuu=lcm(koubaisuu,c);
        }
      for(int i=0;i<A.length;i++){
        B[i]=koubaisuu/A[i];
        }
      int wa=0;
      for(int i=0;i<B.length;i++){
        wa+=B[i];
      }
      System.out.println((int)(wa%(Math.pow(10,9)+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);
}
}