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)

def comb(n, m)
  res = 1
  cnt = 0
  while cnt < m
    res *= n
    n -= 1
    cnt += 1
  end
  while m > 0
    res /= m
    m -= 1
  end
  res
end

require 'prime'
MOD = 1000000007
N, M = gets.split.map(&:to_i)

memo = Hash.new(0)
Prime.prime_division(M).each do |k, v|
  memo[k] += v
end

counter = 1
memo.each do |k, v|
  counter *= comb(v + N - 1, v)
end
p counter % MOD