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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.List;
import java.util.Map;
import java.util.Map.Entry;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.StringTokenizer;

class Main {

    static final int MOD = 1000000007;
    static final int INF = 1 << 30;
    static final int MAX = 1500000;
    static List<Integer> prime;

    public static void main(String[] args) {
        FastScanner sc = new FastScanner(System.in);
        long ans = 0;
        int N = sc.nextInt();
        int[] a = sc.nextIntArray(N);
        prime = primeList((int) Math.sqrt(MAX));
        int[] lcm = new int[MAX];
        ArrayList<HashMap<Integer, Integer>> all = new ArrayList<HashMap<Integer, Integer>>();
        for (int i = 0; i < N; i++) {
            final HashMap<Integer, Integer> map = new HashMap<Integer, Integer>();
            all.add(map);
            int n = a[i];
            int c2 = 0;
            while (n != 1 && n % 2 == 0) {
                c2++;
                n >>>= 1;
            }
            if (c2 != 0) {
                map.put(2, c2);
                lcm[2] = Math.max(lcm[2], c2);
            }

            for (int num : prime) {
                int cnt = 0;
                while (n % num == 0) {
                    cnt++;
                    n /= num;
                }
                if (cnt != 0) {
                    map.put(num, cnt);
                    lcm[num] = Math.max(lcm[num], cnt);
                }
                if (num * num > n)
                    break;
            }

            if (n != 1) {
                int index = Arrays.binarySearch(prime.toArray(), n);
                if (index > -1 && index < prime.size() && prime.get(index) == n)
                    lcm[n] = Math.max(lcm[n], 1);
                else {
                    lcm[n] = 1;
                    prime.add(n);
                }
                map.put(n, 1);
            }
        }
        for (int i = 0; i < N; i++) {
            HashMap<Integer, Integer> map = all.get(i);
            // System.out.println(map.toString());
            long pls = 1;
            for (int k : prime) {
                int v = lcm[k];
                if (v == 0)
                    continue;
                int d = v - map.getOrDefault(k, 0);
                pls *= pow(k, d);
                pls %= MOD;
            }
            ans += pls;
            ans %= MOD;
        }
        // System.out.println(Arrays.toString(prime.toArray()));
        System.out.println(ans);
    }

    public static long pow(long x, long n) {
        long sum = 1;
        for (int i = 0; i < n; i++) {
            sum *= x;
            sum %= MOD;
        }
        return sum;
    }

    private static List<Integer> primeList(int max) {
        final List<Integer> prime = new ArrayList<Integer>();
        prime.add(2);
        for (int i = 3; i <= max; i += 2) {
            for (int wari : prime) {
                if (i % wari == 0)
                    break;
                if (wari * wari > i) {
                    prime.add(i);
                    break;
                }
            }
        }
        return prime;
    }
}

class FastScanner {
    private BufferedReader reader = null;
    private StringTokenizer tokenizer = null;

    public FastScanner(InputStream in) {
        reader = new BufferedReader(new InputStreamReader(in));
        tokenizer = null;
    }

    public String next() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public String nextLine() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

        return tokenizer.nextToken("\n");
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }

    public ArrayList<Integer> nextIntList(int n) {
        ArrayList<Integer> a = new ArrayList<Integer>(n);
        for (int i = 0; i < n; i++)
            a.add(nextInt());
        return a;
    }

    public ArrayList<Long> nextLongList(int n) {
        ArrayList<Long> a = new ArrayList<Long>(n);
        for (int i = 0; i < n; i++)
            a.add(nextLong());
        return a;
    }

    public int[] nextIntArray(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = nextInt();
        return a;
    }

    public long[] nextLongArray(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = nextLong();
        return a;
    }
}