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<bits/stdc++.h>
using namespace std;

int isprime(int i){
  int S=sqrt(i);
  int Ans=1;
  for(int j=2; j<=S; j++){
    if(i%j==0){
      Ans=0;
      break;
    }
  }
  return Ans;
}

int main(){
  int N;
  cin >> N;
  vector<int> P(0);
  for(int i=2; i<1000; i++){
    if(isprime(i)==1){
      P.push_back(i);
    }
  }
  int L=P.size();
  vector<int64_t> D(L, 0);
  for(int i=1; i<=N; i++){
    for(int j=0; j<L; j++){
      int M=i;
      while(M%P.at(j)==0){
        D.at(j)++;
        M/=P.at(j);
      }
    }
  }
  int64_t Ans=1;
  for(int64_t i=0; i<L; i++){
    Ans*=D.at(i)+1;
    Ans%=1000000007;
  }
  cout << Ans << endl;
}