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: Runtime Error)

require 'prime'

P = 1_000_000_007

def modPow(x, n)
  if n == 0
    1
  elsif n & 1 == 0
    modPow(x * x % P, n >> 1)
  else
    x * modPow(x * x % P, n >> 1) % P
  end
end

def inv(a)
  modPow(a, P - 2)
end

def nCr(n, r)
  denomi = inv(Frac[n - r]) * inv(Frac[r]) % P 
  Frac[n] * denomi % P
end

def nHr(n, r)
  nCr(n + r - 1, r)
end

N, M = gets.split.map(&:to_i)

xs = M.prime_division.map{|n, i| i}
Frac = (2..(N + xs.max + 1)).inject([1, 1,]) {|ar, x| ar << ar.last * x % P}

ans = 1
xs.each do |x|
  ans = ans * nHr(N, x) % P
end

puts ans