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 Ruby (2.7.1) (judge verdict: Wrong Answer)

require "prime"
class Integer
  def fac
    return 1 if self.zero?
    ary = [*1..self]
    loop do
      return ary[0] if ary.size == 1
      ary = ary.each_slice(2).map{|a| a.size == 2 ? a[0] * a[1] : a[0]}
    end
  end

  def combi(r)
    self.fac / ((r.fac) * ((self - r).fac))
  end
end

n, m = gets.chomp.split.map(&:to_i)
primes = Prime.prime_division(m)

primes.reduce(1) do |sum, prime|
  sum * (prime.last + n - 1).combi(n - 1)
end