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 (1.15.1) (judge verdict: Accepted)

use std::cmp::max;
use std::io::{stdin, Read};

macro_rules! parse {
    ($iter: ident) => {
        $iter.next().unwrap().parse().unwrap()
    };
    ($iter: ident,2) => {
        (parse!(iter), parse!(iter))
    };
    ($iter: ident,3) => {
        (parse!(iter), parse!(iter), parse!(iter))
    };
    ($iter: ident,4) => {
        (parse!(iter), parse!(iter), parse!(iter), parse!(iter))
    };
}

fn gcd(a: u64, b: u64) -> u64 {
    match b {
        0 => a,
        _ => gcd(b, a % b),
    }
}

const MOD: u64 = 1000000007;

fn powmod(base: u64, exp: u64, m: u64) -> u64 {
    let b: Vec<bool> = format!("{:b}", exp)
        .chars()
        .map(|x| x.to_digit(10).unwrap() != 0)
        .collect();
    let mut v = 1;
    for bi in b {
        v *= v;
        v %= m;
        if bi {
            v *= base;
            v %= m
        }
    }
    return v % m;
}

fn invmod(x: u64, m: u64) -> u64 {
    powmod(x, m - 2, m)
}

fn prime_factors(x: u64) -> Vec<u64> {
    let mut res = vec![];
    let mut y = x;
    let mut p = 2;
    let upper = (y as f64).sqrt() as u64;
    while y > 1 && p <= upper {
        match y % p {
            0 => {
                res.push(p);
                y /= p;
            }
            _ => {
                p += 1;
            }
        }
    }
    if y > 1 {
        res.push(y)
    }
    return res;
}

fn main() {
    let mut s = String::new();
    stdin().read_to_string(&mut s).unwrap();
    let mut iter = s.split_whitespace();
    let _: u64 = parse!(iter);
    let a: Vec<u64> = iter.map(|x| x.parse().unwrap()).collect();
    let mut pv = vec![0; 1000000];
    for ai in &a {
        let mut prev = 0;
        let mut count = 0;
        for p in prime_factors(*ai) {
            if p == prev {
                count += 1;
            } else {
                pv[prev as usize] = max(pv[prev as usize], count);
                prev = p;
                count = 1;
            }
        }
        pv[prev as usize] = max(pv[prev as usize], count);
    }
    let l = pv
        .into_iter()
        .enumerate()
        .fold(1, |x, (i, y)| (x * powmod(i as u64, y, MOD)) % MOD);
    let res = a
        .iter()
        .fold(0, |x, y| (x + (l * invmod(*y, MOD)) % MOD) % MOD);

    println!("{:}", res);
}