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'

MAX = 10**6
MOD = 10**9 + 7

@fac = []
@faci = []
@inv = []

@fac[0] = @fac[1] = 1
@faci[0] = @faci[1] = 1
@inv[1] = 1

2.upto(MAX) do |i|
  @fac[i] = @fac[i - 1] * i % MOD
  @inv[i] = MOD - @inv[MOD % i] * (MOD / i) % MOD
  @faci[i] = @faci[i - 1] * @inv[i] % MOD
end

def comb(n, k)
  return 0 if n < k
  return 0 if n < 0 || k < 0
  return @fac[n] * (@faci[k] * @faci[n - k] % MOD) % MOD
end

n, m = gets.chomp.split(" ").map(&:to_i)

pmd = Prime.prime_division(m)

ans = 1

pmd.each do |pm, e|
  ans *= comb(e + n - 1, e)
  ans %= MOD
end
puts ans