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: Time Limit Exceeded)


import java.util.Scanner;
import java.io.IOException;
import java.io.InputStream;
import java.util.NoSuchElementException;

public class Main {
    public static void main(String[] args){
        long MOD = 7 + (long)1e9;

        FastScanner sc = new FastScanner();
        int n = sc.nextInt();

        int[] primelist = new int[100000];
        int primeNum = 0;
        for(int i = 2 ; i < 1_000_000 ; i++){
            boolean isP = true;
            int sq = (int)Math.sqrt(i);
            for(int k = 2 ; k <= sq ; k++){
                if((i%k) == 0){
                    isP = false;
                    break;
                }
            }
            if(isP){
                primelist[primeNum] = i;
                primeNum++;
            }
        }

        int[] a = new int[10000];
        for(int i= 0 ; i < n ; i++){
            a[i] = sc.nextInt();
        }

        int[] m = new int[100000];
        for(int i = 0 ; i < n ; i++){
            int tar = a[i];
            int p = 0;
            while(tar > 1){
                int pT = 0;
                int pNow = primelist[p];
                while((tar%pNow) == 0){
                    pT++;
                    tar /= pNow;
                }
                if(m[p] < pT){
                    m[p] = pT;
                }

                p++;
            }
        }

        int[] pL = new int[100000];
        int pLNum = 0;
        for(int i = 0 ; i < 100000 ; i++){
            if(m[i] > 0){
                pL[pLNum] = i;
                pLNum++;
            }
        }

        long ans = 0;
        for(int i = 0 ; i < n ; i++){
            int tar = a[i];
            int p = 0;
            long b = 1;
            while(tar > 1){
                int pT = 0;
                int pNow = primelist[pL[p]];
                while((tar%pNow) == 0){
                    pT++;
                    tar /= pNow;
                }
                long mul = 1;
                while(pT < m[pL[p]]){
                    mul = (mul*pNow) % MOD;
                    pT++;
                }

                b = (b * mul) % MOD;
                p++;
            }
            for(; p < pLNum ; p++){
                long mul = 1;
                for(int k = 0 ; k < m[pL[p]] ; k++){
                    mul = (mul*primelist[pL[p]]) % MOD;
                }

                b = (b * mul) % MOD;
            }
            ans = (ans + b) % MOD;
        }

        System.out.println(ans);
    }
}

class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double nextDouble() { return Double.parseDouble(next());}
}