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: Runtime Error)


import java.util.*;
import java.io.*;
class Main {
    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        int N = sc.nextInt();
        int[] a= new int[N];
        int MOD = (int)1e9+7;
        long[] inv = new long[1000005];
        inv[1] = 1;
        for(int i = 2; i<1000005; i++) {
            inv[i] = pow(i,MOD-2,MOD);
        }
        for(int i = 0; i<N; i++) {
            a[i] = sc.nextInt();
        }
        long lcm = a[0];
        for(int i = 1; i<N; i++) {
            lcm = lcm*a[i]*inv[(int)gcd(lcm,a[i])];
            lcm %= MOD;
            //pe(lcm);
        }
        pe(lcm);
        long ans = 0;
        for(int i = 0; i<N; i++) {
            ans += (lcm*inv[a[i]])%MOD;
            ans %= MOD;
            pe("inv "+inv[a[i]]);
            pe((lcm*inv[a[i]])%MOD);
            pe(ans);
        }
        
	p(ans);
    }
    public static long pow(long x, int n, int MOD) { //x^n 計算量O(logn)
		long ans = 1;
		while (n > 0) {
			if ((n & 1) == 1) {
				ans = ans * x % MOD;
			}
			x = x * x % MOD; //一周する度にx, x^2, x^4, x^8となる
			n >>= 1; //桁をずらす n = n >> 1
		}
		return ans%MOD;
	}
    public static long gcd(long num1,long num2) {
        if(num2>num1) {
            long tmp = num2;
            num2 = num1;
            num1 = tmp;
        }
        if(num2==0) return num1;
        else return gcd(num2,num1%num2);
    }
    public static <T> void p(T element) {
	System.out.println(element);
    }
    public static <T> void pe(T element) {
        System.err.println(element);
        }
    public static int min(int a, int b, int c) {
	int min = Math.min(a,b);
	min = Math.min(min,c);
	return min;
    }
    public static int max(int a, int b,int c) {
	int max= Math.max(a,b);
	max = Math.max(max,c);
        return max;
    }
}
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 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());
    }
}