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 ncr(n, r)
  r = [r, n - r].min
  return 1 if r == 0
  return n if r == 1
  numerator = (n - r + 1..n).to_a
  denominator = (1..r).to_a
  (2..r).each{|p|
    pivot = denominator[p - 1]
    if pivot > 1
      offset = (n - r) % p
      (p - 1).step(r - 1, p){|k|
        numerator[k - offset] /= pivot
        denominator[k] /= pivot
      }
    end
  }
  result = 1
  (0..r - 1).each{|k|
    result *= numerator[k] if numerator[k] > 1
  }
  return result
end

n, m = gets.split
n = n.to_i
m = m.to_i

factors = m.prime_division
as = factors.map { |x| x[1] }


ans = 1
for a in as
    ans = ans * ncr(a + n - 1, n - 1) % 1000000007
end

puts ans