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.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		try (Scanner sc = new Scanner(System.in)) {
			// nがあり、nの数だけの整数の入力
			long n = sc.nextLong();
			List<Long> an = new ArrayList<>();
			for (long i = 0; i < n; i++) {
				an.add(sc.nextLong());
			}
			long lcm = an.get(0);
			for (int i = 1; i < an.size(); i++) {
				lcm = lcm(lcm, an.get(i));
			}
			long result = 0;
			for (int i = 0; i < an.size(); i++) {
				long wkResult = lcm / an.get(i);
				wkResult = wkResult % 1000000007l;
				result = result + (lcm / an.get(i));
				result = result % 1000000007l;
			}
			System.out.println(result);
		}
	}

	/**
	 * 最小公倍数
	 */
	static long lcm(long a, long b) {
		long temp;
		long c = a;
		c *= b;
		while ((temp = a % b) != 0) {
			a = b;
			b = temp;
		}
		return c / b;
	}
}