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'

MOD = 10 ** 9 + 7
ONE = '1'.freeze

def nCk(n, k)
  res = 1
  i = k
  j = 1
  while i > 0
    res = res * (n - i + 1)
    res %= MOD
    j *= i
    j %= MOD
    i -= 1
  end
  res *= inv(j)
  res %= MOD
  res
end

def repeated_nCk(n, k)
  # 仕切りのイメージで
  nCk(n + k - 1, n - 1) % MOD
end

def inv(x)
  res = 1
  beki = x
  (MOD - 2).to_s(2).reverse.chars do |digest|
    res = (beki * res) % MOD if digest == ONE
    beki = (beki * beki) % MOD
  end
  res
end

n, m = gets.split.map(&:to_i)
factor_counts = m.prime_division.map { |factor, count| count }
puts factor_counts.inject(1) { |res, count| res * repeated_nCk(n, count) } % MOD