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: Time Limit Exceeded)

// AtCoder My Practice
// author: Leonardone @ NEETSDKASU

fn main() {
	let mut stdin = String::new();
    std::io::Read::read_to_string(
    	&mut std::io::stdin(),
        &mut stdin).unwrap();
	let mut stdin = stdin.split_whitespace();
    let mut get = || stdin.next().unwrap();
    
    let n = get().parse::<i64>().unwrap();
    let m = get().parse::<i64>().unwrap();
    
    use std::collections::{HashSet,HashMap};
    
    let mut xs = HashSet::new();
    let mut i = 1;
    while i * i <= m {
    	if m % i == 0 {
        	xs.insert(i);
            xs.insert(m / i);
        }
        i += 1;
    }
    let xs: Vec<_> = xs.iter().collect();
    
    let md = 1_000_000_007;
    
    let mut foo = HashMap::new();
    foo.insert(m, 1_i64);
    for _ in 1..n {
    	let mut bar = HashMap::new();
        for (k, v) in foo.iter() {
        	for &c in xs.iter() {
            	if k % c != 0 {
                	continue;
                }
                let k = k / c;
                let e = bar.entry(k).or_insert(0);
                let w = (*e + v) % md;
                *e = w;
            }
        }
        foo = bar;
    }
    let mut ans = 0;
    for v in foo.values() {
    	ans = (ans + v) % md;
    }
    println!("{}", ans);
    // println!("{:?}", foo);
}