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 (2.3.3) (judge verdict: Time Limit Exceeded)

require 'prime'

class Integer
  def combination(k)
    self.factorial/(k.factorial*(self-k).factorial)
  end
  def permutation(k)
    self.factorial/(self-k).factorial
  end
  def factorial
    return 1 if self == 0
    (1..self).inject(:*)
  end
end

n, m = gets.split.map(&:to_i)
pd = m.prime_division

div = 10 ** 9 + 7
count = 1
pd.each do |_, k|
  count = count * ((n + k - 1).combination(k) % div) % div
end
puts count