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: Time Limit Exceeded)

DBG = true
require 'prime'

R = 1000000007

def factorialp(n, q)
  ((n-q+1)..n).inject(1,:*)
end

def comb(n,q)
  return factorialp(n,q) / (factorialp(q,q))
end

def ff(q,k)
  if k == 0
    return 1
  elsif k == 1
    return q
  elsif q == 1
    return 1
  else
    sum = 0
    for i in 0..k
      sum += ff(q-1, k-i)
    end
    return sum
  end
end

def f(q,k)
  return ff(q, k-q)
end

def h(n, k)
  sum = 0
  #if n > k
    for q in 1..[k,n].min
      sum += (f(q,k) * comb(n,q)) % R
    end
  #else
  #  for q in 1..k
  #    sum += f(q,k) % R
  #  end
  #end
  return sum
end

def g(n,m)
  facs = m.prime_division
  prod = 1
  for i in 0...facs.size
    prod = (prod * h(n, facs[i][1])) % R
  end
  return prod
end

# # # # main # # # #

n,m = gets.split.map{|x| x.to_i}
print g(n,m)