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 Rust (1.42.0) (judge verdict: Accepted)

#![allow(unused_imports)]
use std::cmp::*;
use std::collections::*;
use itertools::Itertools;
use num::clamp;
use proconio::{input, marker::*, fastout};
use superslice::*;
use num_bigint::*;
use num_traits::{Zero, One};

#[fastout()]
fn main() {
    input! {
        n: usize,
        a: [u64; n]
    }
    let m = 1_000_000_007u64.to_biguint().unwrap();

    let mut l = a[0].to_biguint().unwrap();
    for &v in &a {
        l = lcm(l, v.to_biguint().unwrap());
    }

    let mut ans: BigUint = Zero::zero();
    for &v in &a {
        let v = v.to_biguint().unwrap();
        ans += (l.clone() / v) % m.clone();
        ans %= m.clone();
    }
    println!("{}", ans);
}
#[allow(dead_code)]
pub fn gcd(a: BigUint, b: BigUint) -> BigUint {
    if b == Zero::zero() {
        a
    } else {
        gcd(b.clone(), a % b)
    }
}
#[allow(dead_code)]
pub fn lcm(a: BigUint, b: BigUint) -> BigUint {
    a.clone() / gcd(a, b.clone()) * b
}