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 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define sz(x) int(x.size())
using namespace std;
typedef long long ll;
typedef pair<int, int> P;

const ll INF = 1LL << 60;

ll N;
vector<ll> A;

// 最大公約数
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }

// 最小公倍数
ll lcm(ll a, ll b) { return a / gcd(a,b) * b; }

const int mod = 1e9 + 7;

int main() {
    cin >> N;
    A.resize(N);
    rep(i, N) cin >> A[i];

    ll lcm_v = 1;
    rep(i, N) {
        lcm_v = lcm(lcm_v, A[i]);
    }

    ll ans = 0;
    rep(i, N) {
        ans += lcm_v / A[i];
        ans %= mod;
    }
    cout << ans << endl;
}