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)

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


# factorize m
fs = []
2.upto(Math.sqrt(m).ceil) do |i|
  cnt = 0
  while m % i == 0
    m /= i
    cnt += 1
  end

  fs << cnt if cnt != 0
end

if m != 1
  fs << 1
end

total = 1
fs.each do |f|
  comb = Array.new(n + 1, 1)

  fmax = f

  fmax.times do
    1.upto(comb.size - 1) do |i|
      comb[i] = comb[i] + comb[i - 1]
    end
  end

  total *= comb[n - 1]
  total %= 1_000_000_007
end

p total