Problem:
Score : 400 points

Problem Statement

You are given positive integers N and M.

How many sequences a of length N consisting of positive integers satisfy a_1 \times a_2 \times ... \times a_N = M? Find the count modulo 10^9+7.

Here, two sequences a' and a'' are considered different when there exists some i such that a_i' \neq a_i''.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

1 \leq M \leq 10^9

Input

Input is given from Standard Input in the following format:

N M

Output

Print the number of the sequences consisting of positive integers that satisfy the condition, modulo 10^9 + 7.

Sample Input 1

2 6

Sample Output 1

4

Four sequences satisfy the condition: \{a_1, a_2\} = \{1, 6\}, \{2, 3\}, \{3, 2\} and \{6, 1\}.

Sample Input 2

3 12

Sample Output 2

18

Sample Input 3

100000 1000000000

Sample Output 3

957870001

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::collections::HashMap;
use std::io;
use std::vec::Vec;

const MOD: i64 = 1000000007;

fn modinv(a: i64, n: i64) -> i64 {
    let mut t = (0, 1);
    let mut r = (n, a);
    while r.1 != 0 {
        t = (t.1, t.0 - (r.0 / r.1) * t.1);
        r = (r.1, r.0 % r.1);
    }
    while t.0 < 0 {
        t.0 += n
    }
    t.0
}

fn main() {
    let mut l = String::new();
    io::stdin().read_line(&mut l).expect("");
    let l = l
        .trim()
        .split(" ")
        .map(|x| x.parse().expect(""))
        .collect::<Vec<i64>>();
    let (n, mut m) = (l[0], l[1]);
    let mut h = HashMap::new();
    let mut i = 2;
    while i * i <= m {
        if m % i == 0 {
            h.insert(i, 1);
            m /= i;
            while m % i == 0 {
                if let Some(x) = h.get_mut(&i) {
                    *x = *x + 1
                }
                m /= i;
            }
        }
        if i % 2 == 0 {
            i += 1
        } else {
            i += 2
        }
    }
    if m > 1 {
        h.insert(m, 1);
    }
    let mut r = 1;
    for (_, &v) in h.iter() {
        let mut k = 1;
        for i in 0..v {
            k = k * (n + i) % MOD
        }
        let mut l = 1;
        for i in 2..v + 1 {
            l = (l * i) % MOD
        }
        r = r * (k * modinv(l, MOD) % MOD) % MOD
    }
    if r < 0 {
        r += MOD
    }
    println!("{}", r)
}