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'
N,M=gets.chomp.split(" ").map { |e| e.to_i }

a=M.prime_division

def comb(n,x)
  c = 1
  a = 1
  for i in 1..x do
    c *= n
    a *= i
    n = n-1
  end
  return c/a
end



def sum_prime_number(a,n)
  leng = a.length
  sum = 1
  for i in 0..leng-1  do
    sum *= comb(a[i][1]+n-1,a[i][1])
  end

return sum

end

sum = sum_prime_number(a,N)

puts sum % (10**9+7)