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 Go (1.6) (judge verdict: Accepted)

package main

import (
	. "fmt"
	"io"
	"os"
)

// github.com/EndlessCheng/codeforces-go
func run(_r io.Reader, _w io.Writer) {
	const p int = 1e9 + 7
	pow := func(x int) int {
		res := 1
		for n := p - 2; n > 0; n >>= 1 {
			if n&1 == 1 {
				res = res * x % p
			}
			x = x * x % p
		}
		return res
	}
	c := func(n, k int) int {
		if k > n-k {
			k = n - k
		}
		a, b := 1, 1
		for i := 1; i <= k; i++ {
			a = a * n % p
			n--
			b = b * i % p
		}
		return a * pow(b) % p
	}
	var n, m int
	Fscan(_r, &n, &m)
	ans := 1
	for i := 2; i*i <= m; i++ {
		e := 0
		for ; m%i == 0; m /= i {
			e++
		}
		if e > 0 {
			ans = ans * c(e+n-1, n-1) % p
		}
	}
	if m > 1 {
		ans = ans * n % p
	}
	Fprint(_w, ans)
}

func main() { run(os.Stdin, os.Stdout) }