Problem:
Score : 300 points

Problem Statement

You are given an integer N.
Find the number of the positive divisors of N!, modulo 10^9+7.

Constraints

1≤N≤10^3

Input

The input is given from Standard Input in the following format:

N

Output

Print the number of the positive divisors of N!, modulo 10^9+7.

Sample Input 1

3

Sample Output 1

4

There are four divisors of 3! =6: 1, 2, 3 and 6. Thus, the output should be 4.

Sample Input 2

6

Sample Output 2

30

Sample Input 3

1000

Sample Output 3

972926972

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <vector>
#define MOD 1000000007

using namespace std;

int main(void) {
	int i, j, num, buf;
	long long ans = 1;
	vector<int> pri = { 2 }, d = { 0 };
	cin >> num;
	for (i = 3; i <= num; i+=2) {;
		j = 0;
		while (j < pri.size() && i % pri[j] != 0)
			j++;
		if (j == pri.size()) {
			pri.push_back(i);
			d.push_back(0);
		}
	}
	for (i = 0; i < pri.size(); i++) {
		buf = 1;
		while (num / buf >= 1) {
			buf *= pri[i];
			d[i] += num / buf;
		}
	}
	for (i = 0; i < d.size(); i++) {
		ans *= d[i] + 1;
		ans %= MOD;
	}
	cout << ans << "\n";
	return 0;
}