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 Rust (1.15.1) (judge verdict: Accepted)

#[allow(unused_imports)]
use std::char::from_digit;
#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::fs::File;
#[allow(unused_imports)]
use std::io::prelude::*;
#[allow(unused_imports)]
use std::io::{stdin, stdout, BufReader, BufWriter, Stdin, Stdout, Write};
#[allow(unused_imports)]
use std::mem::swap;
#[allow(unused_imports)]
use std::str::FromStr;

type BoxResult<T> = Result<T, Box<std::error::Error>>;

const MOD: u64 = 1_000_000_000 + 7;

fn main() {
    let mut scanner = Scanner::new(stdin());
    let n = scanner.read::<usize>().unwrap();
    let primes = count_primes(n);
    let mut ans = 1;
    for p in primes {
        let mut count = 0;
        let mut val = p;
        while val <= n {
            count += n / val;
            val *= p;
        }
        ans *= count as u64 + 1;
        ans %= MOD;
    }
    println!("{}", ans);
}

fn count_primes(n: usize) -> Vec<usize> {
    let mut is_prime = vec![true; n + 1];
    let mut primes = vec![];
    for i in 2..(n + 1) {
        if !is_prime[i] {
            continue;
        }
        primes.push(i);
        for j in 1..(n / i + 1) {
            is_prime[i * j] = false;
        }
    }
    primes
}

#[allow(dead_code)]
struct Scanner<R> {
    reader: BufReader<R>,
    buffer: String,
}
impl<R> Scanner<R>
where
    R: Read,
{
    #[allow(dead_code)]
    fn new(inner: R) -> Scanner<R> {
        let reader = BufReader::new(inner);
        let buffer = String::new();
        Scanner {
            reader: reader,
            buffer: buffer,
        }
    }
    #[allow(dead_code)]
    fn with_capacity(capacity: usize, inner: R) -> Scanner<R> {
        let reader = BufReader::with_capacity(capacity, inner);
        let buffer = String::new();
        Scanner {
            reader: reader,
            buffer: buffer,
        }
    }
    #[allow(dead_code)]
    fn read_line(&mut self) -> BoxResult<String> {
        self.reader.read_line(&mut self.buffer)?;
        let cloned = self.buffer.trim().to_string();
        self.buffer.clear();
        Ok(cloned)
    }
    #[allow(dead_code)]
    fn read<T>(&mut self) -> BoxResult<T>
    where
        T: FromStr,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let parsed = self.buffer.trim().parse()?;
        self.buffer.clear();
        Ok(parsed)
    }
    #[allow(dead_code)]
    fn read_two<T, U>(&mut self) -> BoxResult<(T, U)>
    where
        T: FromStr,
        T: Copy,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
        U: FromStr,
        U: Copy,
        U::Err: std::fmt::Debug,
        U::Err: std::error::Error,
        U::Err: 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let (a, b) = {
            let params = self.buffer.trim().split_whitespace().collect::<Vec<_>>();
            let a = params[0].parse()?;
            let b = params[1].parse()?;
            (a, b)
        };
        self.buffer.clear();
        Ok((a, b))
    }
    #[allow(dead_code)]
    fn read_three<T>(&mut self) -> BoxResult<(T, T, T)>
    where
        T: FromStr,
        T: Copy,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        let nums = self.read_vector()?;
        Ok((nums[0], nums[1], nums[2]))
    }
    #[allow(dead_code)]
    fn read_vector<T>(&mut self) -> BoxResult<Vec<T>>
    where
        T: FromStr,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let parsed_vec = self
            .buffer
            .trim()
            .split_whitespace()
            .map(|s| s.parse())
            .collect::<Result<Vec<_>, _>>()?;
        self.buffer.clear();
        Ok(parsed_vec)
    }
    #[allow(dead_code)]
    fn read_matrix<T>(&mut self, lines: usize) -> BoxResult<Vec<Vec<T>>>
    where
        T: FromStr,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        let mut parsed_matrix = vec![];
        for _ in 0..lines {
            self.reader.read_line(&mut self.buffer)?;
            parsed_matrix.push(
                self.buffer
                    .trim()
                    .split_whitespace()
                    .map(|s| s.parse())
                    .collect::<Result<Vec<_>, _>>()?,
            );
            self.buffer.clear();
        }
        Ok(parsed_matrix)
    }
    #[allow(dead_code)]
    fn read_chars(&mut self) -> BoxResult<Vec<char>> {
        self.reader.read_line(&mut self.buffer)?;
        let chars = self.buffer.trim().chars().collect::<Vec<_>>();
        self.buffer.clear();
        Ok(chars)
    }
}