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;

long long MOD=1000000007LL;

int main(){
	int N;
	long long ans=1;
	cin >> N;
	
	map<int,long long> m;
	
	vector<bool> prime(1001,true);
	prime[1]=false;
	for(int i=2;i<=1000;i++){
		if(prime[i])for(int j=i+i;j<=1000;j+=i)prime[j]=false;
	}
	
	for(int i=1;i<=1000;i++){
		if(prime[i])m.insert(make_pair(i,0LL));
	}
	
	for(int i=2;i<=N;i++){
		int k=i;
		for(int p=2;p*p<=k;){
			if(k%p==0){
				k/=p;
				m[p]++;
			}else p++;
		}
		if(k>1)m[k]++;
	}
	
	for(auto p:m){
		ans*=p.second+1;
		ans%=MOD;
	}
	cout << ans << endl;
	return 0;
}