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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

const MOD = 1000000007

var sc = bufio.NewScanner(os.Stdin)

func init() {
	sc.Split(bufio.ScanWords)
}

func nextInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

func Max(x ...int) int {
	max := x[0]
	for _, v := range x {
		if v > max {
			max = v
		}
	}
	return max
}

func Min(x ...int) int {
	min := x[0]
	for _, v := range x {
		if v < min {
			min = v
		}
	}
	return min
}

func GCD(a, b int) int {
	x := Min(a, b)
	y := Max(a, b)
	for {
		t := y % x
		if t == 0 {
			return x
		}
		y = x
		x = t
	}
}

func LCM(a, b int) int {
	// return (a % MOD * b % MOD) % MOD * ModInv(GCD(a, b), MOD) % MOD
	gcd := GCD(a, b)
	return a * b / gcd
}

func ModInv(a, m int) int {
	b := m
	u := 1
	v := 0
	for b != 0 {
		t := a / b
		a -= t * b
		a, b = b, a
		u -= t * v
		u, v = v, u
	}

	u %= m
	if (u < 0) {
		u += m
	}

	return u
}

func main() {
	n := nextInt()
	a := make([]int, n)
	for i := 0; i < n; i++ {
		a[i] = nextInt()
	}

	lcm := a[0]
	for i := 1; i < n; i++ {
		lcm = LCM(lcm, a[i])
	}

	total := 0
	for i := 0; i < n; i++ {
		b := lcm % MOD * ModInv(a[i], MOD)
		total = (total % MOD + b % MOD) % MOD
	}

	fmt.Printf("%d", total)
}