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>
#include <algorithm>
#include <cmath>
#include <queue>
#include <limits>
#include <map>
#define REP(i,n) for(long (i)=0;(i)<(n);(i)++)
#define REPI(i,a,b) for(long (i)=(a);(i)<(b);(i)++)
#define INF numeric_limits<double>::infinity()
constexpr long MOD = 1e9 + 7;
using namespace std;
using P = pair<long, long>;
using VI = vector<long>;

int d[1001];

void hoge(int n) {
    int i = 2;
    while (n != 1) {
        while (n % i == 0) {
            n /= i;
            d[i]++;
        }
        i++;
    }
}

int main() {
    long n;
    cin >> n;
    for (int i = n; i >= 2; i--) hoge(i);
    long ans = 1;
    REPI(i,2,n+1) {
        if (d[i]) {
            ans *= d[i] + 1;
            ans %= MOD;
        }
    }
    cout << ans << endl;
}