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(non_snake_case)]
#![allow(unused_variables)]
#![allow(dead_code)]

fn main() {
    let N: usize = {
        let mut line: String = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        line.trim().parse().unwrap()
    };

    const MOD: i64 = 1_000_000_007;
    fn modinv(x: i64) -> i64 {
        let mut a = x;
        let mut b = MOD;
        let mut u = 1;
        let mut v = 0;
        while b != 0 {
            let t = a / b;
            a -= t * b;
            std::mem::swap(&mut a, &mut b);
            u -= t * v;
            std::mem::swap(&mut u, &mut v);
        }
        u %= MOD;
        if u >= 0 { u } else { u + MOD }
    }
    #[derive(Copy, Clone)]
    struct ModInt {
        x: i64
    }
    impl ModInt {
        fn new(x: i64) -> ModInt {
            let y = if x >= 0 {
                x % MOD
            } else {
                (x + (1 - x / MOD) * MOD) % MOD
            };
            ModInt {x: y}
        }
    }
    impl std::ops::Add<ModInt> for ModInt {
        type Output = ModInt;
        fn add(self, other: ModInt) -> ModInt {
            ModInt::new(self.x + other.x)
        }
    }
    impl std::ops::Add<i64> for ModInt {
        type Output = ModInt;
        fn add(self, other: i64) -> ModInt {
            ModInt::new(self.x + other)
        }
    }
    impl std::ops::Add<usize> for ModInt {
        type Output = ModInt;
        fn add(self, other: usize) -> ModInt {
            ModInt::new(self.x + (other as i64))
        }
    }
    impl std::ops::Sub<ModInt> for ModInt {
        type Output = ModInt;
        fn sub(self, other: ModInt) -> ModInt {
            ModInt::new(self.x - other.x)
        }
    }
    impl std::ops::Sub<i64> for ModInt {
        type Output = ModInt;
        fn sub(self, other: i64) -> ModInt {
            ModInt::new(self.x - other)
        }
    }
    impl std::ops::Sub<usize> for ModInt {
        type Output = ModInt;
        fn sub(self, other: usize) -> ModInt {
            ModInt::new(self.x - (other as i64))
        }
    }
    impl std::ops::Mul<ModInt> for ModInt {
        type Output = ModInt;
        fn mul(self, other: ModInt) -> ModInt {
            ModInt::new(self.x * other.x)
        }
    }
    impl std::ops::Mul<i64> for ModInt {
        type Output = ModInt;
        fn mul(self, other: i64) -> ModInt {
            ModInt::new(self.x * other)
        }
    }
    impl std::ops::Mul<usize> for ModInt {
        type Output = ModInt;
        fn mul(self, other: usize) -> ModInt {
            ModInt::new(self.x * (other as i64))
        }
    }
    impl std::ops::Div<ModInt> for ModInt {
        type Output = ModInt;
        fn div(self, other: ModInt) -> ModInt {
            ModInt::new(self.x * modinv(other.x as i64))
        }
    }
    impl std::ops::Div<i64> for ModInt {
        type Output = ModInt;
        fn div(self, other: i64) -> ModInt {
            ModInt::new(self.x * modinv(other))
        }
    }
    impl std::ops::Div<usize> for ModInt {
        type Output = ModInt;
        fn div(self, other: usize) -> ModInt {
            ModInt::new(self.x * modinv(other as i64))
        }
    }
    impl std::fmt::Display for ModInt {
        fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
            write!(f, "{}", self.x)
        }
    }

    let mut p = vec![ModInt::new(0); N + 1];
    for k in 2..(N + 1) {
        let mut j = k;
        for i in 2..(k + 1) {
            while j % i == 0 {
                j /= i;
                p[i] = p[i] + 1i64;
            }
        }
    }

    let ans = p.iter().map(|&p| p + 1i64).fold(ModInt::new(1), |res, p| res * p);

    println!("{}", ans);
}