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: Runtime Error)

# 2 6   n m
require 'prime'

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

array_prime_division = m.prime_division
array_p = []
array_b = []
array_prime_division.each do |p, b|
  array_b << b
end

fact_n_pred = fact(n-1)

ans = 1
array_b.each do |b|
  comb = 1
  b.times do |j|
    comb *= (b+n-1-j) / (b-j)
  end

  ans *= comb
end

p ans