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: Accepted)

require 'prime'

def mod_combi(n, m)
  return mod_combi(n, n-m) if n-m < m;

  ans = 1
  for i in 0...m do
    ans *= n - i;
    ans /= i + 1;
  end
  # puts "#{n} #{m} -> #{ans}"
  ans
end

mod = 10**9 + 7;
n, m = STDIN.gets.split(" ").map(&:to_i)
factors = m.prime_division

ans = 1
factors.each do |v, pow|
  ans *= mod_combi(n+pow-1, n-1)
end
puts ans % mod