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)

#![allow(unused_parens)]
#![allow(unused_imports)]
#![allow(non_upper_case_globals)]

#[allow(unused_macros)]
macro_rules! invec {
    ( $ t : ty ) => {{
        let mut s = String::new();
        match std::io::stdin().read_line(&mut s) {
            Ok(0) => Vec::<$t>::new(),
            Ok(n) => s
                .trim()
                .split_whitespace()
                .map(|s| s.parse::<$t>().unwrap())
                .collect::<Vec<$t>>(),
            Err(_) => Vec::<$t>::new(),
        }
    }};
}

#[allow(unused_macros)]
macro_rules! get {
      ($t:ty) => {
          {
              let mut line: String = String::new();
              std::io::stdin().read_line(&mut line).unwrap();
              line.trim().parse::<$t>().unwrap()
          }
      };
      ($($t:ty),*) => {
          {
              let mut line: String = String::new();
              std::io::stdin().read_line(&mut line).unwrap();
              let mut iter = line.split_whitespace();
              (
                  $(iter.next().unwrap().parse::<$t>().unwrap(),)*
              )
          }
      };
      ($t:ty; $n:expr) => {
          (0..$n).map(|_|
              get!($t)
          ).collect::<Vec<_>>()
      };
      ($($t:ty),*; $n:expr) => {
          (0..$n).map(|_|
              get!($($t),*)
          ).collect::<Vec<_>>()
      };
      ($t:ty ;;) => {
          {
              let mut line: String = String::new();
              std::io::stdin().read_line(&mut line).unwrap();
              line.split_whitespace()
                  .map(|t| t.parse::<$t>().unwrap())
                  .collect::<Vec<_>>()
          }
      };
      ($t:ty ;; $n:expr) => {
          (0..$n).map(|_| get!($t ;;)).collect::<Vec<_>>()
      };
}

#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let mut s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
    ($iter:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($next:expr, [$t:tt]) => {
        {
            let len = read_value!($next, usize);
            (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        }
    };
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

#[cfg(debug_assertions)]
macro_rules! mydbg {
    //($arg:expr) => (dbg!($arg))
    //($arg:expr) => (println!("{:?}",$arg));
      ($($a:expr),*) => {
          eprintln!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
      }
}
#[cfg(not(debug_assertions))]
macro_rules! mydbg {
    ($($arg:expr),*) => {};
}

use std::cmp::*;
use std::collections::*;
use std::ops::{Add, Div, Mul, Sub};

#[allow(dead_code)]
static INF_I64: i64 = 92233720368547758;
#[allow(dead_code)]
static INF_I32: i32 = 21474836;
#[allow(dead_code)]
static INF_USIZE: usize = 18446744073709551;

#[derive(Debug, Copy, Clone)]
pub struct ModInt {
    x: i64,
    global_mod: i64,
}
impl ModInt {
    pub fn new(p: i64) -> Self {
        let gm = 1000000007;
        let a = (p % gm + gm) % gm;
        return ModInt {
            x: a,
            global_mod: gm,
        };
    }
    pub fn inv(self) -> Self {
        return self.pow(self.global_mod - 2);
    }
    pub fn pow(self, t: i64) -> Self {
        if (t == 0) {
            return ModInt::new(1);
        };
        let mut a = self.pow(t >> 1);
        a = a * a;
        if (t & 1 != 0) {
            a = a * self
        };
        return a;
    }
}
impl Add for ModInt {
    type Output = ModInt;
    fn add(self, other: ModInt) -> ModInt {
        let ret = self.x + other.x;
        return ModInt::new(ret);
    }
}
impl Sub for ModInt {
    type Output = ModInt;
    fn sub(self, other: ModInt) -> ModInt {
        let ret = self.x - other.x;
        return ModInt::new(ret);
    }
}
impl Mul for ModInt {
    type Output = ModInt;
    fn mul(self, other: ModInt) -> ModInt {
        let ret = self.x * other.x;
        return ModInt::new(ret);
    }
}
impl Div for ModInt {
    type Output = ModInt;
    fn div(self, other: ModInt) -> ModInt {
        let ret = self.x * other.inv().x;
        return ModInt::new(ret);
    }
}
impl std::string::ToString for ModInt {
    fn to_string(&self) -> String {
        return self.x.to_string();
    }
}
pub struct Combination {
    fact: Vec<ModInt>,
    ifact: Vec<ModInt>,
}
impl Combination {
    pub fn new(n: i32) -> Self {
        let mut fact = vec![ModInt::new(0); (n + 1) as usize];
        let mut ifact = vec![ModInt::new(0); (n + 1) as usize];
        fact[0] = ModInt::new(1);
        for i in 1..n + 1 {
            fact[i as usize] = fact[(i - 1) as usize] * ModInt::new(i as i64)
        }
        ifact[n as usize] = fact[n as usize].inv();
        for i in (1..n + 1).rev() {
            ifact[(i - 1) as usize] = ifact[i as usize] * ModInt::new(i as i64)
        }
        let a = Combination {
            fact: fact,
            ifact: ifact,
        };
        return a;
    }
    #[macro_use]
    pub fn gen(self, n: i32, k: i32) -> ModInt {
        mydbg!(self.fact[n as usize]);
        mydbg!(self.ifact[k as usize]);
        mydbg!(self.ifact[(n - k) as usize]);
        if (k < 0 || k > n) {
            return ModInt::new(0 as i64);
        };
        return self.fact[n as usize] * self.ifact[k as usize] * self.ifact[(n - k) as usize];
    }
}

pub struct PrimeFactor {
    base: u64,
    exp: u64,
}
impl PrimeFactor {
    fn new(base: u64, exp: u64) -> PrimeFactor {
        PrimeFactor {
            base: base,
            exp: exp,
        }
    }
}
impl PartialEq for PrimeFactor {
    fn eq(&self, target: &Self) -> bool {
        self.base == target.base && self.exp == target.exp
    }
}
impl Eq for PrimeFactor {}

pub struct Sieve {
    primes: Vec<i64>,
    sieve: Vec<i64>,
}

impl Sieve {
    pub fn new(size: usize) -> Self {
        let mut kusi = vec![0_i64; size];
        let mut primes = vec![];
        kusi[0] = -1;
        kusi[1] = -1;
        for i in 2..size {
            if kusi[i] == 0 {
                primes.push(i as i64);
                let mut k = i;
                while k < size {
                    kusi[k] = i as i64;
                    k += i;
                }
            }
        }

        Sieve {
            primes: primes,
            sieve: kusi,
        }
    }
    pub fn isPrime(&mut self, x: usize) -> bool {
        return self.sieve[x] == x as i64;
    }

    pub fn factrize(&mut self, mut x: i64) -> Vec<PrimeFactor> {
        let mut a = vec![];
        while x > 1 {
            let b = self.sieve[x as usize];
            x /= b;
            a.push(b);
        }

        let mut ret: Vec<PrimeFactor> = vec![];
        let mut p = 0;
        for i in 0..a.len() {
            if p != a[i] {
                ret.push(PrimeFactor::new(a[i] as u64, 1));
                p = a[i];
            } else {
                //PrimeFactor::new(ret[ret.len() - 1].base, ret[ret.len() - 1].exp + 1);
                let l = ret.len();
                ret[l - 1].exp += 1;
            }
        }
        return ret;
    }
}

fn main() {
    input! {
       n: usize,
       mut a:[u64;n],
    }

    let mut sieve = Sieve::new(1000006);

    let mut f = a.iter().map(|x| sieve.factrize(*x as i64));
    let mut x = HashMap::new();
    for item in f {
        for item2 in item {
            let key = item2.base;
            match x.get(&key) {
                Some(&v) => {
                    let new = max(v, item2.exp);
                    x.insert(key, new);
                }
                None => {
                    x.insert(key, item2.exp);
                }
            }
        }
    }

    mydbg!(x);

    let mut y = ModInt::new(1);
    for (base, exp) in x.iter() {
        mydbg!(base, exp);
        y = y * ModInt::new(*base as i64).pow(*exp as i64);
    }
    mydbg!(y.x);

    let ans = a
        .iter()
        .map(|x| y / ModInt::new(*x as i64))
        .fold(ModInt::new(0), |acc, x| x + acc);

    println!("{}", ans.x);
}