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)

nu1,nu2 = gets.chomp.split(" ").map(&:to_i)
li = 1 + (nu2**0.5).to_i
check = []
require 'prime'
if nu2 == 1
  puts 1
  exit
end

Prime.each(li) do |prime|
  check.push(prime)
end
nu3 = nu2
count = 0
divi = []
check.each do |x|
  while nu3 % x == 0
    nu3 /= x
    count += 1
  end
  if count > 0
    divi.push(count)
    count = 0
  end
  if nu3 == 1
    break
  end
end
if nu3 != 1
  divi.push(1)
end

leng = divi.length


ans = 1
for i in 0..leng - 1
  for j in 1..divi[i]
    ans *= (divi[i] + nu1 - j) % (10**9 + 7)
    ans /= j
  end
  ans %= 10**9 + 7
end

p ans