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)

// Utilities
import java.io.*;
import java.util.*;
import java.math.*;

public class Main {
  static int N;
  static int[] a;
  static BigInteger res = new BigInteger("0");
  static BigInteger lcm = new BigInteger("1");
  static final int MOD = (int)1e9 + 7;

  public static void main(String[] args) throws IOException {
    INPUT in = new INPUT(System.in);
    N = in.iscan(); a = new int[N];
    for (int i = 0; i < N; i++) {
      a[i] = in.iscan();
      lcm = UTILITIES.lcm(lcm, a[i], MOD);
    }
    for (int i = 0; i < N; i++){
      res = res.add(lcm.divide(BigInteger.valueOf(a[i]))).mod(BigInteger.valueOf(MOD));
    }
    System.out.println(res);
  }

  private static class INPUT {
 
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar, numChars;
 
		public INPUT (InputStream stream) {
			this.stream = stream;
		}
 
		public INPUT (String file) throws IOException {
			this.stream = new FileInputStream (file);
		}
 
		public int cscan () throws IOException {
			if (curChar >= numChars) {
				curChar = 0;
				numChars = stream.read (buf);
			}
			
			if (numChars == -1)
				return numChars;
 
			return buf[curChar++];
		}
 
		public int iscan () throws IOException {
			int c = cscan (), sgn = 1;
			
			while (space (c))
				c = cscan ();
 
			if (c == '-') {
				sgn = -1;
				c = cscan ();
			}
 
			int res = 0;
 
			do {
				res = (res << 1) + (res << 3);
				res += c - '0';
				c = cscan ();
			}
			while (!space (c));
 
			return res * sgn;
		}
 
		public String sscan () throws IOException {
			int c = cscan ();
			
			while (space (c))
				c = cscan ();
 
			StringBuilder res = new StringBuilder ();
 
			do {
				res.appendCodePoint (c);
				c = cscan ();
			}
			while (!space (c));
 
			return res.toString ();
		}
 
		public double dscan () throws IOException {
			int c = cscan (), sgn = 1;
			
			while (space (c))
				c = cscan ();
 
			if (c == '-') {
				sgn = -1;
				c = cscan ();
			}
 
			double res = 0;
 
			while (!space (c) && c != '.') {
				if (c == 'e' || c == 'E')
					return res * UTILITIES.fast_pow (10, iscan ());
				
				res *= 10;
				res += c - '0';
				c = cscan ();
			}
 
			if (c == '.') {
				c = cscan ();
				double m = 1;
 
				while (!space (c)) {
					if (c == 'e' || c == 'E')
						return res * UTILITIES.fast_pow (10, iscan ());
 
					m /= 10;
					res += (c - '0') * m;
					c = cscan ();
				}
			}
 
			return res * sgn;
		}
 
		public long lscan () throws IOException {
			int c = cscan (), sgn = 1;
			
			while (space (c))
				c = cscan ();
 
			if (c == '-') {
				sgn = -1;
				c = cscan ();
			}
 
			long res = 0;
 
			do {
				res = (res << 1) + (res << 3);
				res += c - '0';
				c = cscan ();
			}
			while (!space (c));
 
			return res * sgn;
		}
 
		public boolean space (int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
	}
 
	public static class UTILITIES {
 
		static final double EPS = 10e-6;
 
		public static int lower_bound (int[] arr, int x) {
			int low = 0, high = arr.length, mid = -1;
 
			while (low < high) {
				mid = (low + high) / 2;
 
				if (arr[mid] >= x)
					high = mid;
				else
					low = mid + 1;
			}
 
			return low;
		}
 
		public static int upper_bound (int[] arr, int x) {
			int low = 0, high = arr.length, mid = -1;
 
			while (low < high) {
				mid = (low + high) / 2;
 
				if (arr[mid] > x)
					high = mid;
				else
					low = mid + 1;
			}
 
			return low;
		}
 
		public static long gcd (long a, long b) {
			return b == 0 ? a : gcd (b, a % b);
		}
 
		public static BigInteger lcm (BigInteger a, long b, long mod) {
			return a.multiply(BigInteger.valueOf(b)).divide(BigInteger.valueOf(gcd(a.longValue(), b)));
		}
 
		public static long fast_pow_mod (long b, long x, long mod) {
			if (x == 0) return 1;
			if (x == 1) return b;
			if (x % 2 == 0) return fast_pow_mod (b * b % mod, x / 2, mod) % mod;
 
			return b * fast_pow_mod (b * b % mod, x / 2, mod) % mod;
		}
 
		public static long fast_pow (long b, long x) {
			if (x == 0) return 1;
			if (x == 1) return b;
			if (x % 2 == 0) return fast_pow (b * b, x / 2);
 
			return b * fast_pow (b * b, x / 2);
		}
 
		public static long choose (long n, long k) {
			k = Math.min (k, n - k);
			long val = 1;
 
			for (int i = 0; i < k; ++i)
				val = val * (n - i) / (i + 1);
 
			return val;
		}
 
		public static long permute (int n, int k) {
			if (n < k) return 0;
			long val = 1;
 
			for (int i = 0; i < k; ++i)
				val = (val * (n - i));
 
			return val;
		}
	}
}